The closing process (also referred to as settlement) could warrant a full page to itself. But for now, it's suffice to say that the closing process requires a lot of paperwork, the settling of any outstanding fees or costs, and the transfer of the deed to the new owner.
The best way to prepare for this process is by asking a lot of questions leading up to settlement, staying in close contact with your agent and the escrow / settlement company, and making sure you have some cash put aside for final expenses.
At the end of this process, the seller will hand over the keys to the property and you officially become the new owner of the property!