Here's a direct link to the instructions from the College Board as to how to install. Below are the steps with some visual reference.
1. Install LockDown Browser from AP Classroom website (this can also be done directly from the App Store or Self-Service). From AP Classroom, select LockDown Browser link, then select iPad Edition.
2. Download LockDown Browser from App Store.
3. Set-up the app. First, type school name. Then, allow the app to install.
4. Now, you need to verify the installation. This can be done on AP Classroom prior to use or in conjunction with an assignment. Both are shown below. Regardless of method, follow instructions that prompt you to close apps and modify security settings (these are referenced in second image).
Best of luck!