Varispeed is useful if you need to change the overall tempo of your project of tracks you recorded. Apple loops
and midi will follow the tempo you initiate, so if you done vocals or live guitar normally you would re record. Varispeed will make it all match at once and save the hassle of re recording. Now if your talking about beat matching pre recorded tracks to follow tempo varispeed wont help. Right click on Global Tracks and add Tempo and Beat Mapping. Now make sure both tracks are at full view tilting the arrows. Now you will need the main track in your song to build a tempo map from ( may be drums, hi hat, guitar etc). Once selected, in the beat map track press the button detect. Now you should see markers placed at the transients in the region your creating the map from.
Above that you will see the Beat Markers from your inital tempo. Now line up your transient Markers with your Beat Markers by clicking the beat measure and drag it to the transient you want to align it to. Now you will notice in the tempo track the tempo begins to change with each edit as you have all the markers where you need them. This sometimes can be a long process depending on your project, most time this is used in orchestrated live recorded sesions, but hey i dont know your project.
Now if your having your recored tracks playing a little out of time Then use Flex Time.
press command key then F . Flex mode by default is off. Click on off and select slicing. Now every transient has a marker to place in time. You can quantize the audio as you would in midi from the inspector bar or manually create markers and move them yourself. On Apples website for Logic,they have videos to show you how it works in great detail.