I agree with Keno about inclusive culture. It you are accepting, you should have a diverse staff and not really test to see if someone fits (other than the no-a-hole rule).
A few things that I found help:
lunches. Eating together builds a team. Pot lucks are fun for getting some discussions going too.
Be honest to the nature of the group. Organizing an after work laser-tag competition is not for every team. The team activities need to come from within the team.
The leader needs to be a bit of a mirror. A leader who boasts culture all the time and then follows their own rules is doomed to lose the respect of the team.