In addition to a thermometer you can use the "touch" method which takes some getting used to and is difficult to explain clearly via text:
Touch the tip of your ring finger to your thumb. Then with the index finger on your other hand touch the fleshy portion between the thumb and index finger on the hand that has the ring finger and thumb touching. The fleshy portion should feel more firm than soft, this is about the way that medium-well should feel in meat. If your turkey burger feels the same way, it should be done.
As for other doneness using this method:
-Hand open loose = rare
-index finger to thumb = medium rare
-middle finger to thumb = medium
-ring finger to thumb = medium well
-little finger to thumb = well done (aka "shoe leather")
Note that for some people there can be very little difference in firmness of the muscle changes as you switch fingers so it's something that really mainly comes with experience for most people using the "touch method".
This is only for individual cuts/burgers etc. Roasts and whole birds require a thermometer.