Try using the L1 button instead, to immediately take close control, and turn into space.
Or, use R2 and drag the Left analogue stick diagonal to the direction you want to go - this gives you a side-step, and should set you off running at medium pace.
Don't hit R2 until you have actually received the ball, otherwise your player will just let the ball go past him, between his legs.
If you can get the timing right, and once your comfortable with the direction each move will take you in, you can start to play passes to players so that they can consistantly turn into space.