You stop watching the meter spin and start watching the bill shrink to almost nothing. The actual installation on your roof takes just a couple of days, but getting it done right means booking during the off-season for contractors when quotes are typically lower. Spring and late fall are usually the best times to get trades out before the summer rush hits.
Before you commit to anything, you need to get at least three different quotes from local installers. Solar pricing varies wildly between companies for the exact same hardware, and comparing bids is the only way to avoid overpaying for the system.
Remember that the intro window is a strict deadline, not free money. If you still have a remaining balance when the 15 months end, the standard interest rate kicks in immediately on the whole original amount.