Here are the steps I would take:
- Make sure you understand the group's current goals.
- Get together with just the new player and work together to design a character that has at least one common interest with the other characters.
- Still with the new player, design a scene where the new player meets the party.
- On your own, design a scenario where the new player contributes to the party.
Now here's an example of all this in practice:
- The party is a tightly-knit bunch of brawlers and swordsmen, all from the same town, trying to track down the evil wizard who burned their hometown to the ground. Currently they've found out where one of his evil wizard buddies is at, causing some sort of ruckus in a village in the woods.
- You get together with the new player and explain what the party's up to. Together, you come up with a character: a young wizard who was orphaned (by the evil wizard, though the character doesn't know that), then taken in and taught the art of magic by a kindly old man (the same wizard, of course), but then fled when he realized that the old man was actually a bad guy. This new character doesn't have a goal yet, but he has a common interest with the party -- stopping the evil wizard.
- Now it's game night, and the party is in the woods near the village where the evil wizard's evil buddy is hanging out. While they're busy checking out the village from afar before going in, they find someone else in the woods doing the same thing -- a mighty paladin, eight feet tall, a grand defender of peace and justice, come to defeat the wizard. But the illusion falls flat, and soon enough the party sees through it. It's just a teenage kid, but one who's amazingly good with magic for being so young. Introductions all round, turns out everyone's there to see what evil deeds are afoot.
- The party's in town, and they make an attempt to get into the bad guy's hideout. Having a wizard in tow turns out to be pretty helpful, as he can recognize all kinds of dangerous things that a bunch of fighters might never know about.
After just one session, the new character has both found some good allies and proven his worth to them. If the new player decides to stay in the game after that night, it'll be very easy for their character to be a regular part of the group.
Addendum: To encourage this sort of group cohesion, the game I'm running has two particular rules:
- Your character must be connected in some way to one of the other characters.
- If your character gets to a point where they can't be part of the group anymore, it's time to make a new character.
A new player joined halfway through our current campaign, so she had to make a character with a connection to one (or more) of the characters in the group. She decided her character was from the same village as one of the other characters, and that she had personally witnessed an event in the past that the party was investigating. Her goal was to look for the same villain as the party and to defend their common homeland.
Another player had a character that gradually became more and more in league with the evil river spirit in the story. The rest of the party, meanwhile, was working for the enemy of that river spirit. Once the difference of purpose had gotten too great, we sat down and talked about our options. He could betray the river spirit and join goals with the rest of the party, or he could play a different character. His old character went to a heroic death (that the group still talks about) and a new character was born.