Hey there, neighbor.
They just changed the process here, everything goes through the sheriff's office on county house road, turn off of RTE 5 at 84 Lumber, or off of Rte 34 at Owens Illinois (near pick-n-pull).
On your 21st birthday, head out there between 8:00 and 4:30, mon-fri. pick up an application. Also, sign up for the class at Bass Pro, get the first class after your 21st, they are $25 and I think held the last Tuesday evening of every month.
Once you have the application filled out, and the class certificate, and the various money orders you need (they are listed on the application), take the application back to the sheriff and they will process it in 6-8 weeks and send it over to the judge for approval. The judge will sign off on it and you'll get an unrestricted lifetime CCW.
Part of the application is listing 4 references, they have to not be related to you or each other, nd they can't have the same address as you or each other, also they need to live in Cayuga co. Once you turn the application in, the sheriff will mail simple questionaires out to them, which they have to fill out and mail back. I saw one and it is basic stuff like "How long have you know this person" etc. MAKE SURE YOUR REFERENCES MAIL THEM BACK! In fact, have the 4 of them over for dinner and a fill-out party, provide stamped envelopes and everything.