How long after the first vaccine can you go back to having sex or do you have to wait for all three?

At least 2 shots: The vaccination process against the HPV infection was initially proposed to be 3 injections over 6 months. More recently FDA has advised that 2 vaccines seem to provide sufficient protection such that the 3rd injection(given at 6 month point) may not be necessary. So you should take your 2nd vaccination, usually done after 2 months of the first shot, before having sexual intercourse.

Understand the shot: This shot can/will help your body develop some protection against some strains of a common STD. It will take time for the protection to kick in (months) and is limited to the few strains of germs in the shots. Your best protection against STD's is common sense, with a condom helping some. It does not protect you against the germs you were already exposed to, or those not part of the shot.