Look we've all been their, maybe a new friend wants to join your game, maybe someone died and they need a new character, either way the story is started and game is going and you need to bring in someone new. For lots of games the answer is simple, you just have the party come across the new character and it's understood that they will join the group. Sometimes a new character just shows up as if they were there all along. I won't lie I'm not a fan of this as it stretches your suspension of disbelief and can even make for choices that players characters would never make for the sake of one player getting into the game. In my games I take a somewhat brutal approach to bringing in new characters, but it also guarantees an organic growth of story while bringing new characters into the fold.
Rule 1: No one is Forced to accept you.
This is where many will start claiming "Player Freedom", but it's a pretty simple concept. The other members of the party are under no obligation to invite you on their adventure. This means if you don't make a character the rest of the group would get along with or that would have no business either being with these people or interested in their quest your character might only last one scene before the group moves on leaving you behind.
Yes this means that the rest of the party is the deciding factor in what YOU get to be, but they are a team and you need to pass tryouts if you want to play. There are ways to make this easier though that I will bring in later.
Rule 2: No one just appears.
One thing that always bugs me is the scenario where the party is in a dungeon, not just any dungeon but one that hasn't been searched in generations. Last session Greg over there died to a trap and he has rolled up a new character. The party enters an unexplored room and there's Greg's new character. I don't care the reasoning or if he's fighting for his life or a prisoner of the cult inside that dungeon hasn't been explored in generations and unless the GM has story reasons for that to even be possible then he simply wouldn't be there.
This means multiple sessions can go by till a new character even shows up let alone is invited to the group (see Rule 1).
Rule 3: Help is appreciated.
OK, so this isn't a rule as much as a suggestion, but it's an important one. Talk to your other players and work together to figure out the character. Remember, you character has to be someone the rest of the group likes and has to be somewhere the group is going that will have people. This means that working with the group is your single best chance at success. That isn't to mean let them make the character for you, but definitely listen to their ideas and what they might be looking for in a party member.
Rule 4: The Master Rule
This one is simple, the GM can tell you no. Just like characters at the beginning of a campaign the GM can feel free to look over your character call bull shit and toss it out. Yes this is a lot of power, but the GM has a lot of power. He (or she) might know things about the game world or story you don't. He also gets to say your pink bunny ninja has no place in his game. IF you feel this is unfair also remember that your character shows up when the GM feels they would naturally show up and if you want to skip or worse ignore this rule be prepared to wait and become the groups waiter as everyone else gets characters.
Bonus Rule: The Trial Character
This is more for new players coming to join the game for the first time. They might have never played a game or they might just be new to the group. Either way I don't let them make a character on their first day out. Sometimes if I'm feeling like it or if I really think the player will stick around as GM I make a simple NPC for them to play. Usually has enough HP or Toughness to hang with the group, has a reason to be in this sessions story but the story doesn't hinge on it, and most importantly can be gone by next session. If I'm feeling lazy or think a full character might be a bit much for them I just give them a generic guard. Has the same stats as any other guard or goon or what have you for the setting, but it's role played by the player.
This protects a few things. First the basic NPC or Guard usually only requires basic knowledge of the rules, a simple attack, how defense works, basic stats, and maybe a couple skills. These are training wheels for new players and a mussel for experienced players coming to a new table. Since a town guard could have any personality it lets the player show what personality they might bring to the table and how they interact with the group. An added benefit of using a guard or police officer is it can function as a small litmus test on if that player abuses small amounts of power or athority and how they might wield it. Finally the character is disposable, this means if they do something stupid and get killed they can just pick up another guard (if you want them to) and more importantly if they turn out to be a flake or such a problem you don't want them back the NPC can still exist under GM control or just vanish and the story doesn't grind to a halt or cause a moment when they parties new friend just seems to be gone (something I find as immersion breaking as a character just showing up for no reason.)
Hopefully this helps some of you out there bring new characters into your games more naturally.