If the new player is known by someone in the group and is recommended as a good addition, I generally invite them on a trial basis after meeting them. That's the best way to go and generally the most successful.
However, when I've needed to find a new player or two from the world at large, I use a formal interview screening process with three steps, after posting on forums and local gaming stores. The process (similiar to a job interview) starts with 1) an email list of standard questions which I then review the responses with the group, 2) phone conversation, and 3) an in person meeting with myself and possibly one other person from the group. If the player commits through all the steps and seems like a good match, I invite them to join us on a trial basis. Then I make sure to check with the group as well as the new player to see if it's a good fit, if there are areas that need attention, or if it's just not the right mix.
While the process involves a little more work all around, it's definitely worth it in my opinion. I've found the process ultimately saves the group time in the long run in finding the best fit and it saves new players time as well--we are roleplay intensive, serious about the gaming experience and there are plenty of people who prefer a different style of play. Plus the fact the fact the process is a bit lengthier (requires a few hours of the new candidate's time) works as an advantage: players unwilling to commit a few hours to the interview process certainly aren't going to commit the time to the campaign (at least in my experience). Usually each of the three "steps" I use cut the field of candidates by 50% to 65%.
I've been using this process for about 12 years (refining it as I go) and am usually successful at finding good candidates, but even still, it boils down to the new person having the right "chemistry" with the existing group. It doesn't always work, but I firmly believe it works much better than a cattle-call approach for my group, given the wide variety of styles of play and the vastly different things many players like to experience in a campaign.