Watch the entire video in full with the out-of-sync audio. On a piece of paper or notepad, make note of any time throughout the video that the audio goes out of sync. Often times the entire video will be off, but only small sections need fixing.
Use the timeline in your video editor to navigate to the first out-of-sync section. Find a piece of dialog near this section with a very pronounced syllable, such as a "P" or "T" being said. Move the marker to the exact spot that this syllable is spoken.
In the audio timeline, look for the closest waveform spike (a spot where the waveform of the audio is larger and more pronounced than other places) and play the audio from this point. If it is the syllable you are looking for, move the timeline backward or forward so that this spike lines up with the point in the video that it is spoken.
Play the video from this point forward. The audio in this section should be perfectly in sync. When you come to the next out-of-sync time that you wrote down, check that it is in sync after the first change. If not, break the audio with the "split" function at this point and line up the audio in a similar fashion to the first section.
When you've fixed the audio in each out-of-sync section in the video, play the entire movie back in its entirety, looking for other spots that may have gone out of sync due to the changes you've made. Be sure to fix these before exporting your video.