What are Finger Tricks?
Finger tricks are used in speedcubing for two main reasons: They increase your speed considerably and are a way to show off your skills. Basically, it is method of solving the Rubik's cube by turning the different sections using a flick of the finger. It Is also about knowing the correct sequences of turns and flicks to achieve common moves as fast as possible. Those skilled at finger tricks will never let go of the cube with their hands.
Lubricate
Before you begin practicing finger tricks and speedcubing, you will need a Rubik's cube that is as loose as possible. This means that new cubes are less desirable; the more mileage, the better. If you don't have an old cube or you want to make your loose cube even looser, try this: Partially dismantle the cube and spray the inside with lubricant. Finger tricks require much more physical strain on the fingers than normally solving a Rubik's cube and so anything that relieves this is a good thing. Mainly though, it decreases your speedcubing solving time.
The UR' Trick
Hold the cube in your left hand in the standard grip, which is between your thumb and middle finger. The fewer fingers you use to hold the cube, the more free fingers you have to perform tricks and increase your speed. Put your index finger on the left of the upper-left square on the back of the cube. Back is the side that your middle finger is on. Flick the upper face here so it moves 90 degrees clockwise. As soon as it reaches its destination pull the right face down 90 degrees in an counterclockwise direction. Plenty of practice turns these two moves into one motion.
U'L Trick
Grab the cube in your right hand using the standard grip. Rest your index finger on the right side of the upper-right piece on the back of the cube. Flick the upper face 90 degrees counterclockwise. Flip the left face 90 degrees clockwise just as the first turn falls into position. As with the previous trick, turning this into one fluid movement is highly important.