Sync issues are *usually* going to be mismatched sample rates, for instance, you imported 44.1kHz audio into a 48kHz project.
This happened to me awhile back, and unfortunately, I don't remember exactly what I did to fix it. But what I *think* I did was click on the imported audio and went to the Retime menu and selected Conform Speed. If that doesn't work, right click on the audio in the event browser and select Transcode (if there's an option to do so in the dialog).
It is also possible to manually resync audio by Retiming it. Turn on snapping (N), select the clip, type Command-R and drag the audio clip's retiming handle until the end of the audio snaps with the end of the video clip (this is actually amazingly accurate.) [If your recorded audio is not the same length of the audio on the video, then set markers on the video and audio tracks and retime until the markers snap.] You should do this before any other edits.
Yes, it's often the sample rate, as Fox says 44.1 vs 48khz. If you click on your audio track in the event Browser, in "list view" you can right-click on the columns and add an "audio sample rate" column, you'll be able to see what your audio track is.
Then, open the "project library" and highlight your project. In the inspector, click on the little tool icon (bottom right) "modify project properties" and you can change your project's sample rate to match your audio clip. You may have to restart FCPX to get it to conform, but then you should be back in sync - if that was indeed your problem.