Running
Use your left thumb to move Grag or Thog by placing your thumb down anywhere on the left-hand side of the screen and sliding it to the left or right. Once Grag or Thog begin running in a direction, you do not need to keep sliding your finger, simply keep it depressed. To stop, just lift your thumb.
Jumping
Using your right thumb, simply swipe upwards anywhere on the right half of the screen. You do not need to use large sweeping motions, a simple upwards flick will do it.