How to sync motion and music in After Effects
Depends on how much time stretch is key to synchronize the shot. 


In order to increase the speed of the whole layer use the Time Stretch feature (Right Click the Layer > Time > Time Stretch) Note: values below 100 increase the speed. Values above 110 often results in bad quality. To solve this, see motion calculation (3.)   
To vary the speed of a layer, it's ok in most cases to use the standard Time Remapping feature (Right Click the Layer > Time > Enable Time Remapping) This makes it possible to keyframe the time/speed of your layer.
In some situations, especially for generating slow motion shots you need to calculate the motion in between the frames with optical flow technology like twixtor. You can also play with SlomoVideo as an open source alternative. For further information, see this article: http://www.fxguide.com/featured/art_of_optical_flow/




For audio preview workflow, see: How can I preview with audio in After Effects and be able to pause / resume the preview?