Step 1: Visit http://www.unrealtournament.com
Step 2: Click the Download button in the top right corner.
Step 3: If you have an account, sign in and it will let you download the launcher. If you do not, it will bring up a quick signup form that you can fill out.
Step 4: Download the Launcher.
Step 5: Open the launcher. When you open the launcher, it should look something like this:
Step 6: There are tabs at the top. Click the Unreal Tournament tab. Where my picture says Launch, there will be the option to Launch or if needed, Download/Update UT. If you played earlier builds, keeping up with new ones was tedious work. With the Launcher, it does all of the work for you and staying up to date is as easy as clicking a button.
Step 7: Open the game and shoot the guns.