The process for restoring an iPad from an iCloud backup begins by wiping the iPad, which puts it into the same clean state it was when you first got it out of the box. But before you take this step, it is a good idea to make sure your iPad is being backed up to the iCloud. (Obviously, this won't be possible in certain circumstances, such as restoring a brand new iPad with your old iPad's data and settings.)
You can verify your iCloud backup by going into the iPad's settings and choosing iCloud from the left-side menu. In the iCloud settings, choose Storage and Backup. This will take you to a screen that will display the last time the iPad was backed up to iCloud.
Once you verify the backup, you are ready to begin the process. You will start by erasing all data and settings from the iPad, which puts it into a clean state. You can do this by going to the iPad settings and choosing General from the left-side menu. Scroll all the way down the General settings until you see "Reset". From this menu, choose "Erase All Content and Settings".
Once the iPad finishes erasing the data, you will be taken to the same screen you were at when you first got your iPad. As you set up the iPad, you will be given the choice to restore the iPad from a backup. This option appears after you have signed into your Wi-Fi network and chosen whether or not to use location services.
When you choose to restore from a backup, you will be taken to a screen where you can choose from your last backup or other backups, which is usually your last three or four backups.
Note: If you are restoring from a backup because you have run into problems with your iPad that can only be solved by restoring it, you can first choose your latest backup. If you still have problems, you can move on to the next latest backup, repeating the process until (hopefully) the problem is cleared.
Restoring from a backup can take some time. The process uses your Wi-Fi connection to download settings, content and data. If you had a lot of content on your iPad, this can take a while. The restore screen should give you estimates at each stage of the restore process, starting with restoring the settings and then booting into the iPad. When the iPad home screen appears, the iPad will continue the restore process by downloading all of your applications.
If you do run into a problem with this stage, you can always download an application again from the app store for free. You can also sync apps from iTunes on your PC. But the iPad should be able to restore all of your applications on its own. Remember, if you have a lot of apps, it could take some time for the iPad to complete this step. In addition to downloading apps, the process restores photos and other data, so if it doesn't look like there is progress, the iPad could be working on downloading more than just apps.