How many times does a ger tovel (immerse) when converting? I know that a ger immerses first then makes the bracha (can't make the bracha yet until the person becomes a Jew). Does the ger then immerse again after this a second time? If so why/what is the source for this?
A convert actually immerses three times, according to Rabbi Maurice Lamm here:
There is one exception to this general practice of placing the blessing before the mitzvah--the immersion of a convert. The convert needs to recite the blessing after the immersion, not before. The reason is simple: One cannot declare "God commanded us" if one is not commanded by God because he or she is not Jewish. The convert becomes a Jew only after the immersion is completed.
After the blessing, the convert immerses twice more and then leaves the mikveh.
A second blessing is required by most, but not all, authorities. It is called she'hecheyanu, and with it a person thanks God that He has enabled him to live to experience the greatness of this moment.
I don't know his sources, but I know that this is the practice in my local community.