The amount of months before your next upgrade all depends on which carrier and early upgrade plan you have. You typically see early upgrade plans ranging from 6-18 months and sometimes even 24 months on your contracts that are longer than your average 2-year contract.
Click here to Compare iPhone 6s Early Upgrade Plans
If you look at each individual plan, you can notice how many months until your early upgrade. After the amount of months is up, a new early upgrade contract will be issued to get your new phone and then new payments will begin. You have the option to keep your phone but you would probably be placed into another phone payment type category.
You will not own the phone unless you purchase the device outright.
If your contract is 30 months, you are eligible to upgrade after 24 months.
Every other contract term and early upgrade months differ because of prices and plans. If you are paying more for the phone each month you are eligible to upgrade earlier. If you are paying less you are eligible to upgrade at a later month.