I blame Critical Role, but I've seen a lot of conversation about new characters on various RPG discussion boards I frequent. It makes sense. A lot of people just watched a 5 year campaign end, have heard teases of the new game to start, and want to know what is going on. Some places are even cautioning against going for something complex and deep from the bat, and that is also good advice. With all of it going on, I can't help but put my own two cents in. So consider this my advice for starting a new character.
Just trust me on this, but you want to start simple and you'll have the most chance to have fun if you do. Start with a simple concept. For some games - like D&D - that can be as easy as a Race/Class combination. For other games - like L5R - it can mean your school and family/clan. For more open games it can mean a lot of things but generally starting with a sex/race/job is a good place to start.
This is your character in the simplest terms, and they are common first choices you have to make just to build a character. The idea here isn't to trap yourself in anything beyond the role you will fulfill mechanically in the game. Even the most beautiful of paintings will start out as a single line on the page, so don't go for Leonardo's finest work from the get go. We'll get there, for now just draw that first line.
Backgrounds Add A Little Depth
One of the things I love about D&D 5E is that Background is a mandatory part of the character. You don't just start as a level 1 fighter, you're a level 1 fighter with a background. Maybe that means you spent time as a sailor - frequently hailed as the most useful background - or you did a stint as a charlatan. Perhaps you were a hermit, a soldier, a criminal. It doesn't matter, it adds more detail to the character and begins to tell a story. A fighter who started life as a Criminal, and one who started life as a Soldier are likely two very different people, after all.
In other games it can help to give yourself a backstory to explain where your character's training and abilities come from. Like with the concept, keep it simple and vague. Don't throw a lot of details down now, but focus on the broad strokes.
"My character was taught to fight by his father. He headed off to join a mercenary band in search of adventure and excitement. Having gone through a couple wars, he decided he wanted to be his own boss and choose where and when he fought and broke off to go solo."
Boom, we're done, and we have a simple background that tells us all we need for introducing the character to the game.
Add a Quirk, Maybe Two
For further distinction, and to help with getting into character, it can help to add a quirk or maybe two. One of these quirks should be a gesture, or related to an item of clothing. Something you can do or pantomime that helps set the character. If you feel confident, you can do a voice for the character but that's not for everyone.
The idea here is two fold: one) give you a tool to get into character or into a mindset for the character. Two) give your character something to make them a bit more unique from the broad strokes we have without actually detailing too much else.
Small hobbies like wood carving and whittling are great for this. As is playing a musical instrument, constantly adjusting a hat, or fidgeting with a bracelet. Smoking can be another one, as can almost any habit out there. Even a particular way of starting a conversation can do this.
Define and Refine in Game
From there, go to game and see how the character plays out. You have broad strokes, but that leaves you flexible to define things as the game goes on. You can make the character more happy, sad, stoic, or outgoing as you want. You can find what works for the character, the game, and the other players.
Once you get to know the character in play a little bit, you can go back and add more details to your backstory. Talk about it with the GM. Talk about it with other players. But never stop defining, refining, and letting the character grow through game. Stick to this, and when you look back in several months, a year, or later you'll be amazed at how far the character came.
A Note For Pre-Connected Characters
The simple, broad strokes approach may seem counter to pre-connected character concepts, but it can work just fine that way too. You don't need a lot to say two characters are friends going into a game. Just have jobs that work well enough together, and run with it.
If you need more definition rather than defining the character try to define an experience. Make up situations. Have each player make up a situation where their character got in trouble, and have the other character help define how their character helped get the friend out of the situation. By doing this, and one each, you're not defining the person but defining bond making moments. Refer back to those in play. You might be amazed what having even this little bit of shared history can do.
You don't need a detailed sculpture the equal of Sanmartino's Chastity going into the game. You just need a block trimmed down to resemble a humanoid figure. You can carve in all the rest of the details, all the fine touches and breath of life as the game goes on. The best part is, it will be more meaningful for everyone if you do because then everyone sees the growth and is free to grow with the character.