When you have the ball you don't have your arms to help with balance, and the farther the ball is from your centre of gravity the harder it is to pivot, you need a wider base. A key is to bend your knees. A lot of players like to pivot on their non-dominant foot.
a) Jump stop - jog forward on "go", on "stop", jump stop with your dominant foot forward (with parallel feet your upper body keeps going). Be ready to catch a pass each time, and don't jump too high, the feet shouldn't be much off the floor. Continue.
b) Jump stop and pivot - run out, jump stop, pivot (forward pivot on the non-dominant foot), run back, repeat, then pivot the other way (forward pivot on the other foot).
c) Dribble, jump stop and pivot - with a ball, take 2-3 dribbles, jump stop, pivot, dribble back, continue.
d) Spin, catch and pivot - spin a backspin pass 6-7 feet in front of you, catch after one bounce in a jump stop, pivot, repeat.