To put in the new battery, place it in the tray with the positive and negative terminals on the correct sides. Screw on the bracket so the battery is held firmly in place. Place the positive cable clamp over the positive terminal, and tighten the bolt. Connect the negative cable and terminal the same way. Once they're both connected, you can close the hood and start the car.
Since the old battery contains highly toxic material, you must dispose of it properly. Do not treat it like regular garbage. You can dispose of the battery at service garages, auto supply stores (they may offer this service as part of your new battery purchase), and recycling centers. You might be charged a small fee for the service, but it's well worth it.
Once you're finished, drive easy. With the proper maintenance, your car will be using its new battery for years to come.