There's a link to a PDF of the voter registration form and the mailing address on this site:

http://www.cityofboston.gov/elections/voter_reg.asp

Applications must be postmarked 20 days prior to the election, so the deadline for the mayoral election is October 14.

If you have to get a new license, or renew your old one, I'd suggest registering via the RMV.

Personally, I attempted to register to vote a whopping FIVE times before making it onto the voter rolls. Once in person at City Hall when I first moved here, one at a voter reg drive, twice at the polls after not being allowed to vote b/c the other registrations were never recorded for some reason, and then, finally at the RMV, which got me on the voter roll.

I believe that you can now use a universal voter registration form in Boston that you can download from the state's website and mail in. If I remember correctly, when I registered in person at City Hall, I got some sort of receipt or something, which would have helped me if a) I had kept it and b)there had been provisional ballots like we have now at that time.

Hope that helps.