I have a pair of corns that I would like to breed, but I'm not sure where to start. First of all, they have been living in the same cage for about 16 months.
How big are these corns, specifically the female? Like has been said, if that gal isn't up to breedable size yet, you'd be better off separating them until she is. Breeding too young (i.e. at too small of a size) can increase the risk of egg binding and puts a lot of stress on the female.
Also, I'm not sure how to put them into hibernation, or if I need to at all.
Corn snakes do not require brumation (the snake version of hibernation), but it does help you time their cycling. Without brumation, mine have usually bred sometime in February or March on a midwest natural light schedule. It's a lot easier to miss the female's cycle without brumation.
If I leave them together as they are now, will they breed on their own? Or do I need to separate them for a bit then put them back?
Yes, if the female ovulates, the male will breed her. Separating doesn't change that. Again, please please be sure the female is large enough before thinking about breeding them.
On the cohabitation issue, do a search and you'll see numerous, lengthy threads on the subject (you may start with Kathy's FAQ in a thread at the top of the Newsletter forum). My personal opinion is that cohabitation adds stress to the snakes, which may cause no perceivable trouble in some, and may cause problems in others. I don't advocate cohabitation and feel that snakes should be put together only for breeding.
If I do hibernate them, when do I start? Also, when should they be put together for mating?
Most people start brumating right about now and bring them out in 3 to 4 months. Expect the female to come into season for breeding after the 1st or 2nd shed from brumation. Some may go longer, just try them weekly. The male will be very interested when she's ready.