1) Buy a Xenforo License from https://xenforo.com.
2) Download the files from your license and upload them to the root of your domain/subdomain depending on your wanting.
3) Direct yourself to the website you uploaded the files to.
4) You'll see a prompt to "Begin Installation", click that.
5) It will bring up another prompt for a MySQL database, you'll want to direct yourself to the MySQL Database section.
6)
Create a new database named whatever you want, and put the name of the
database in the area that asks for the name of the database.
7) Create a new user named whatever you want, and make the password something that isn't easy guessable.
8)
Next, you'll add the user to the database by scrolling down to the
bottom and click the database you created, and the user you created and
give the user all permissions.
9) After that, enter those credentials into the correct areas, username in the username area, password in the password area.
10) If you did everything correct, once you click Save, it should prompt you with a message saying it worked.
11)
Let it install completely, once it says it was installed and you see a
button that says, "Enter your control center", you're done.