With most ringtone apps, you'll need to sync with iTunes to transfer your free ringtones. Within iTunes, select your iPhone and click on "Apps" in the upper navigation bar. Scroll down and select the correct app. When your ringtone pops up in the "Documents" screen, save it to your desktop.
Now, drag the ringtone from your desktop back into iTunes. It should show up under the "Ringtones" section of your iTunes library. Sync your iPhone.
(Note: Some ringtone apps have slightly different processes for transferring ringtones. For example, some apps will email you the ringtone to save to your computer, so you don't need look for it under the "Apps" tab. Check the directions for your particular app to ensure you are transferring correctly.)