Congratulations, you've reached the home stretch. Just a couple more steps and your car should purr like a kitten once more on the first turn of the ignition.
Lift the new battery and place it into its seat under the hood. By now, you've likely concluded that new batteries are much heavier than old batteries; be careful when lifting.
Your new battery may have come with colored plastic caps on the terminal posts. Don't remove them until you've situated the battery and are ready to attach the terminal cables. These caps will help you remember which post is positive (the red one) and which is negative (the black one).
Once it's situated firmly in its seat, begin the reverse of the operation you undertook to remove the old battery. Start with the positive terminal. Remove the plastic cap and use your battery terminal cleaner to brush the new posts. This will score the metal lightly, which will provide a better grip between the posts and the clamps, which provides easier recharging of your battery while you drive. Spray another coat of corrosion protection on the terminal post. Slide the end clamp over the post until it sits against the bottom of the post. Using your pliers or wrenches, hold the bolt head steady while you tighten the nut in a clockwise direction. Repeat the same steps for the negative terminal.
With both terminals attached, you can now refasten any plate or support that holds your battery in place. While the design of this feature is sometimes a little tricky, don't skip this step. The plates hold the battery in place as your car jostles over rough terrain and speed bumps. Driving with an unattached battery is a bad idea.
At this point, try your car's ignition. It should start right up if your battery was the root of your car's trouble. Since the battery was unattached, you may have lost information in your car's onboard computer. This might require you to re-enter a password for your radio and other features to operate once more.
There's one last step you'll need to take to complete your jaunt into the world of do-it-yourself automotive repair -- disposing of the battery. The combination of lead and acid in car batteries make them toxic waste, so you'll have to take it to the proper recycling center or to a service station, where they will be disposed of for a fee. The store where you bought your new battery might be required to take your old one, depending on what state you live in. Just don't throw it away. Most car batteries are recycled into new ones, preventing toxic contamination of the environment.