Caution: When you are done, do not drop the dumbbells next to you as this is dangerous to your rotator cuff in your shoulders and others working out around you.
Just lift your legs from the floor bending at the knees, twist your wrists so that the palms of your hands are facing each other and place the dumbbells on top of your thighs. When both dumbbells are touching your thighs simultaneously push your upper torso up (while pressing the dumbbells on your thighs) and also perform a slight kick forward with your legs (keeping the dumbbells on top of the thighs). By doing this combined movement, momentum will help you get back to a sitting position with both dumbbells still on top of your thighs. At this moment you can place the dumbbells on the floor.
Another variation of this exercise is to perform it with the palms of the hands facing each other.
Also, you can perform the exercise with the palms facing each other and then twisting the wrist as you lift the dumbbells so that at the top of the movement the palms are facing away from the body. I personally do not use this variation very often as it seems to be hard on my shoulders.