Recruitment

In the beginning of the manga, Luffy claimed that he wanted at least 10 people to join his crew before entering the Grand Line. This was changed after Usopp told Luffy that after "the chef" joined them, they would rescue Nami and go to the Grand Line. Although this is long past the expiring date, it can still serve as evidence that there will be 10 or more Straw Hats at one point of the manga. Luffy also claimed in the beginning of the manga, that he will gather a crew strong enough to surpass his childhood hero Red-Haired Shanks.

Invitation
Usually when he asks someone to join, Luffy is turned down completely and he usually tries to get them to join anyway which more or less gets him and his crew into trouble with marines or other pirates, but has enough moral not to force the person to join against their will. Later on the person in question will join anyways for reasons of their own. The major exceptions to this rule are Usopp, who was thrilled to be asked to join and accepted immediately, and Nico Robin, who invited herself into the crew and had to convince the others to let her stay.

Luffy doesn't seem to mind if someone he wants to recruit has a profession or not. He allows Usopp to join, and later on names him the team's sniper, and considered Vivi a member even though she has no profession. He also offered Gaimon the chance to join his crew (which Gaimon tearfully turned down) when Gaimon had no apparent usefulness to the crew. Also notable is the Gentleman Skeleton Brook, who actually accepted Luffy's initial invitation to join the crew but later claimed that he couldn't honor it due to his lack of a shadow, which would result in his death should he step into sunlight, as well as unfinished business with the zombies of Thriller Bark. However after the Straw Hats and Brook finally defeat these zombies, Brook soon asks if they would honor his initial acceptance, which Luffy did.

Recruiting Process
Though most adventures in One Piece are random, there seems to be a 'process' for recruitment. First, a situation arises where someone new is needed. The crew comes across someone who fulfills the criteria (i.e. Chopper the doctor, Nami the navigator). Luffy offers the person a position, and is usually turned down initially. Meanwhile, a situation arise where, some way or another, Luffy ends up battling a 'boss' character, and the would-be crew mate battles an underling (i.e. Luffy vs Don Krieg after Sanji battles Gin and Pearl), during which their backstory and dreams are revealed, thus convincing them to join the Straw Hat Crew. This process also fooled many fans into thinking Vivi would become a permanent crew member.

The only crew members not following this process were Nami and Robin, both of whose history was revealed later on. Nami's official recruitment was when Luffy, Zoro, Usopp and Sanji defeated Arlong and his pirates. Robin was the first to initially willingly join, and officially after Luffy's crew came to her rescue from CP9. This, however, is still inconclusive. On the other hand, Luffy has recently offered a skeleton named Brook to join the crew when they go into the Florian Triangle. While Brook eventually declined joining (after initially accepting), it has been revealed that he was a former musician for a pirate crew which would fill one of the positions that Luffy wants for his crew.

Luffy has several times stated the need for a musician, because "pirates love music", and thinks of this more important than other positions. Franky, in addition of being a shipwright, plays a guitar. This plea however was finally fulfilled when Brook joined the crew.

Returning to the Crew
If a Straw Hat crew member leaves the crew without Luffy's permission, Luffy usually does his best to recruit them back. So far Robin and Usopp have both left the crew, Robin however rejoined it later. Robin rejoined the crew after they convince her that she should want to live.

While Robin was never on bad terms with the crew when she left Usopp was however a different case. Usopp had officially left the Straw Hat crew, over a dispute concerning the Going Merry yet returned to the crew in his alias "Sogeking" to help rescue Nico Robin. Afterward, Usopp originally planned to make the crew beg for him to return, but Zoro had given the crew a speech about him rejoining them on their terms, not his, and would accept him only if Usopp begged them after a thorough apology. After being ignored while they were fighting off Garp, Usopp finally capitulated and Luffy happily accepted him back (accidently clashing their skulls together in the process).