Logic has always included a pretty comprehensive time stretching engine, in the form of it's 'Pitch and Time Machine'. Although the results gained from using this feature can be excellent, the process is often quite time consuming. If you are looking for a more streamlined method read on!
01 - Identify the Audio you Want to Treat
Home in on the audio region you want to time stretch (or compress) and highlight it. Usually at this point we would need to double click on the part to enter the Sample Editor and use the Time and Pitch Machine. In this case the process can be fully completed within the arrange window.
02 - Perform your Stretch
Grab the end of the part, as if you were going to change the length of the region but while you do this hold down the Option key. At this point you will see the usual resizing cursor change, this indicates you are in time stretch mode.
Now when you resize your part it will time stretch / compress your region accordingly. I find this extremely useful for quickly getting loops or phrases in time. As the stretch tool snaps like any other resizing it's easy to move to correct point.
After a quick progress bar your region is now stretched and you're good to go.
03 - Edit and Mix your Sound
Your region can now be used in the same way as any other sound. You can loop, edit and mix it in the identical fashion and all in under a minute. Super fast time stretching, on the fly... Done!