you need a buddy who will say they had it for at least two years and someone they can say they bought it from
then you need a bill of sale, the dmv is really picky with bills of sale so they get there money for taxes, when registering just say you got it for $200 bucks or something
then you need this, a mv-51 http://www.dmv.ny.gov/forms/mv51.pdf have your buddy fill out his name and address ect ect on the top he will need to put where he bought it from on this form also date of last inspection sticker number and station number can be filled in with N/A since it is a class b moped they did not need to be inspected, max speed is 30mph (class b moped)
then you need a mv-51b http://www.dmv.ny.gov/forms/mv51b.pdf again your buddy will have to fill this out, year of last registration licence plate can all have N/A put in them, these things changed hands so many times they wont give you hell about last plate that was on it or when it was last registered, at the bottom your buddy will have to fill out there name, when they acquired it (remember has to be more than two years ago) and the address and name of who they got it from, make sure you use the same person as you did on the mv-51
after that its just the regular registering vehicle stuff
a dtf-802 http://dmv.ny.gov/forms/dtf802.pdf fill out all your information, vehicle information, your buddys name and address as previous owner information blahblahblah date of transaction ect ect
after that you need a MV-82 http://dmv.ny.gov/forms/mv82.pdf again, fill it out with all the information, if you've registered a car its the same thing you filled out then
lastly you need a "proof of vin" which is annoying... http://www.dmv.ny.gov/proove.htm you can read that but basically you fall in this category near the bottom A pencil tracing, a photo or a police statement that shows the vehicle identification number.
you need a picture of the vin plate where the vin is readable, if it is not readable bring the picture and the ped to the police station, tell them you need a proof of vin, they wont know what that is so you'll have to explain that you need it to register it, they have to sign the picture saying that the vin in the picture is 1111111 or whatever the vin is and there name and date it
once you got ALL of that annoying paperwork out of the way, you need insurance, unless your bike ACTUALLY goes 20mph register it as a class b, top speed of 30mph WITH insurance, its like $100 a YEAR, bring the insurance paper and all of the above to the dmv, pay what they ask ya (usually like 50 bucks) and bam they hand you a registration and a plate, you'll get a transferable registration in the mail shortly if you ever want to sell it!