First off, you need a name. I'd pick something that does NOT sound Japanese, because most of the characters in FMA do not have Japanese names. Anything European-sounding is fine. Unless you want the character to be from Xing, in which case you'd use a Chinese-sounding name. If your character is someone who was from Xerxes, their name can be a little more creative, but I'd avoid using normal names spelled strangely. Ex: Stefany instead of Stephanie, Kristal instead of Crystal, etc. I'd also avoid using a name another character in the series already has. If you're having difficulty thinking of a name, look at some baby-naming websites.
Then you pick their age. Most people make their characters 15-16 so they're close in age to Ed and Al. Unless you want to pair the character up with someone like Roy or Scar or Kimbley... in which case you'd pick an age close to theirs. Roy is 28, Scar is likely older. (I'm not sure of his actual age.) So be sure to keep other characters' ages in mind. If the character is paired with Roy, don't make them a teenager. It's very unlikely that he'd go for that. Unless it's an unrequited love, as in she has a crush on him but he doesn't like her back. Then it's fine to make her younger. (Assuming the character is a girl.) Basically, try to keep them close in age with the characters you will have them spending most of their time with. I doubt some 23 year old would be following a couple of teenagers around (Ed and Al).
Pick a place for them to be from. Risembool, Central, Ishval, Xing. Those are the most popular ones. But remember that there are tons of other places in FMA. You can google "Map of Amestris" and a picture will probably come up with everything mapped out. It's interesting to have characters be from countries that aren't as talked about, like Aerugo, Drachma, and Creta. If you pick a specific origin for them, make sure their personality reflects that. For instance, if they're from Drachma, they're probably used to cold climate and possibly a little rough around the edges. If they're from Resembool, they're probably used to a country lifestyle and have done a lot of manual labor in their lifetime. If they're from Central, they probably have a strong opinion one way or the other about the military, and probably live a busy, urban life. If you want, you can make up a town, or pick one from the series. Just know that if you make up a town, you should pick a region of the country it's in and design what kind of place it is. For example, you could make up a town named Grull between Rush Valley and Dublith. Considering what both of those towns are like, it's probably a pretty busy place that sees a lot of traffic from tourists traveling back and forth between towns. There is also probably a good amount of mechanics in that area, mainly automail mechanics, because it's so close to Rush Valley. Perhaps it's a manufacturing town where all of the tools are made before they're shipped to Rush Valley. What's the weather like most of the year? What kind of people live in this town? Are there factories and/or mines? Is there smog, traffic, etc.?
Decide if he/she has any powers. If you make them a chimera, do NOT give them animal ears or a tail. Keep in mind the other chimeras in FMA do not have those features of their animals. The closest thing is that Law, the Ox chimera, can sprout horns. But Dorochet, the dog chimera, does not have dog ears and a tail. However, he does have fangs and claws like a dog, and the personality of a dog. Martel, the snake chimera, does not have a forked tongue. But she does have the speed, agility, and flexibility of a snake. Unless you make a character that is more like Nina, who was fused with her dog Alexander. In which case, your character would be mostly animal with a few human qualities, such as being able to speak. They probably wouldn't have any physical traits resembling a human, in this case, and they would look pretty much like an animal(s). That might be a bit more limiting, however, than doing it the other way around.
If they are an Alchemist, remember they do not need to be a member of the state. Also, if they are in the military, they do not need to be a State Alchemist. Most people make their OCs State Alchemists. If you do this, try to make their power original. But make sure you are able to explain it scientifically. For example, my OC is the Starlight Alchemist. This is because she makes star-like structures in the air by transmuting the trace amounts of Helium, Hydrogen, and Carbon that are in the air. (Note that you may do something similar to this because the air we breathe is not only Oxygen. There are trace amounts of other elements in it. Note also that you want some kind of unique Alchemic ability, but it HAS to be explainable. This is because Alchemy is a science, and everything can be broken down. It's all about elements.) This is really only necessary if your character is a State Alchemist, however. If they are a soldier who practices alchemy, or just a regular alchemist, they don't necessarily need to have any specific power/type of alchemy they use. It might help, however, with character development, so keep it in mind.
You also need to figure out a look for them. If they are in the military, they might wear the military uniform. But they don't have to, especially if they travel a lot. Also, if they do, note that you should think of a side outfit for them because they likely do not ALWAYS wear the uniform. As for their hair/eye color, you can pretty much give them any color. However, Ishvalans should have red eyes, homunculi should have purple eyes, Xingese people have dark brown/black eyes, and people from Xerxes should have gold eyes.
As far as clothes go, it is all very situational. I'll give a few examples, so pay attention closely.
It depends on if you're designing a guy or girl. For a guy, I'd keep it somewhat simple. But remember not to make it too modern. No graphic t-shirts and jeans. It would have to be most likely a collared shirt or a turtleneck or a tank top and slacks. You could give them a jacket and go into a little detail with that, as long as it suits the style of the series. But don't try to give your OC a coat like Ed's. If you give them a coat, try to make sure it doesn't resemble anyone else's so it's original. Also do NOT under ANY circumstances use a jacket that looks like Ed's. The black one with the metal clamp over the collar. If anyone else wears it, it just looks like you stole it from him and it looks unoriginal. Be CREATIVE and design your OWN clothes. You can look up European/American clothing styles from the late 19th and early 20th centuries, if you need help.
If it's for a girl, I'd say skirts, shorts, or pants. Either leather or khaki or a dark material most likely. If it's a skirt, you could make it pleated considering Winry owns a pleated skirt. But try not to make it look too much like a schoolgirl outfit since they don't have them in FMA. For a shirt, I'd say most people use a tank top and them give them a jacket for versatility. A crop jacket would be cute and it's not often used. (As in a jacket that only goes down to the waist, not the full length of a normal jacket.) But no sweatshirts, it's too modern. Again, don't use too much detail on the actual clothes. But you could use alchemic symbols if you wanted to add some kind of flair. Denim wasn't as popular back then, so it's probably not a good idea. Leather, cotton, suede, etc. are better.
If you want them to be an alchemist, but you need them to have transmutation circles available at all times, you could give them an accessory with the circles engraved/sewn into it like gloves or bracelets or a ring. My character draws them on her hands with a marker, so that's always an option. Or they could use chalk to draw them on the ground. But a lot of people find that it's better for them to have the circles available at all times to have an advantage in battle.
As far as shoes go, most FMA characters wear boots or sandals. Wingtips, loafers, mary-janes, etc. will also work.
If you're designing a girl, don't make her outfit too revealing. She could show a little midriff or cleavage but if you give her a midriff shirt, keep her skirt/pants long. Again, jackets are your friend.
Other accessories a lot of FMA characters utilize are belts, bags, necklaces... but don't use anything strange and modern like fishnet. I've yet to see a single FMA character who wears fishnet. Pantyhose could world, if they work in an office or something, but it isn't realistic for a soldier.
If your character is from Ishval or Xing, be sure to look at the style of the clothes the people from those places wear. Xingese people typically wear more Asian-type clothes. Ishvalans wear more tans and dark colors, but it's more tribal-looking. Lots of shawls and sandals and they cover most of their bodies, probably to protect them from the heat since they live in the desert.
If your OC is in the military, they'll likely wear the uniform a lot of the time. But they should have another outfit for their civilian life. Also, under their uniform, since it's only a jacket and pants, they need a shirt. Roy wears white collared shirts, Riza wears dark, form-fitting t-shirts. I think turtlenecks fit well also and tank tops.
Note also that you may give them automail, but it's wise not to give them a fake right arm and left leg like Ed. Or the opposite, a fake left arm and right leg. You could give them one missing limb or more if you wish. But try not to make it similar to another character. You could even give them a fake eye, like Archer. You can also give them any kind of automail you like. It does not need to look like Ed's. Note Ed and Paninya have different kinds of automail. Also note that Paninya has weapons built into her automail, so you may do that as well if you wish. Don't make your automail look too much like Ed's, because Winry prides herself on her automail being special and different. Unless you have a good excuse for having Winry make your OC's automail, then it might look similar, but still not exactly the same. Try to avoid unnecessary automail, like fingers, toes, ears, etc. It just seems like a reach and it's strange.
Decide if they are human, chimera, or homunculous. If it's a homunculous, note their name should be one of the seven deadly sins, which means you'll have to plan their appearance after one of the existing homunculi dies. Also note that if they are a homunculous, they'll likely wear dark clothes and have pale skin with dark hair and purple eyes. Also they need an oroborus tattoo, but try to put it in a unique place on their body, like no other homunculous has. Not on the chest, like Lust. Not on the thigh, like Envy. Not on the tongue, like Gluttony. And etc.
One thing I must say is that you should NOT under ANY circumstances make them related to any existing characters. This is a very evident Mary Sue trait. Ed and Al do not have any missing siblings that they didn't know about, and Roy does not have a million sisters. They can be friends with whoever you wish them to be friends with, but you should not make them related.
As for their history, note that they do not have to have a horribly tragic past. It does help, however, to develop their character if you are using them in a fanfiction. But you don't have to do that. They can have a home and a family, they can have a pet. They can have friends. Or they can be an orphan who travels because they have no home to go back to. Just try not to make it TOO tragic, if you give them a sad past, because that is another evident Sue trait.
It is not likely that they have performed a human transmutation and lived, because that is nearly impossible to do. That's why Ed and Al are so unique. However, it is possible. So if you REALLY want to have your character have done that, you may. Note also that if they did perform a human transmutation, they have likely seen "The Truth" and have the ability to perform Alchemy without a transmutation circle. But note that if you do that, people may consider your character a Sue because they are more powerful than other characters. If you do this, make sure this character is not more powerful than Ed and Al or Roy because that is a DEFINITE Sue trait.
If your character does use transmutation circles, you may design a unique circle for them depending on their abilities. However that does take a lot of research. For example, Roy's circle has a salamander on it. This is because in Alchemy, the salamander is a symbol of fire. Obviously, Arakawa did her research when she made this anime. It's one of the reasons I admire her so much. But anyway, you may construct a unique circle for them or you may use one you've seen in the show. Also, they should have some sort of accessory or easy access to their circle since they may not have time to draw one if they're in a battle. My OC draws them on her hands with a marker. Other characters have bracelets or rings with their circles etched into them. Roy has his gloves. My friend's OC uses a gun with explosive bullets and she carves the circles onto the bullets so she can use Alchemy to make the gunpowder in them explode.