Are you playing on X-Box, PS3, or PC?

First, you can only have one of those powers selected at a time, but they're a separate selection from your hand-abilities (your sword, your bow, your fire spell, whatever). Once you have one selected, you simply press a button to activate it.

On the PC you press Z (at least in my version). I think the X-Box is one of the front trigger buttons, the little ones in front of the main triggers. I have no idea what it is on the PS3, but it should be something. It should be the same button you use to activate your dragon power shouts, like Unrelenting Force.

And that's it. Hit the button to activate the selected power, be it Beast Form or Dragon Shouts or your daily racial power. Most of these powers have some sort of cooldown associated with them, meaning you can only use them once every X seconds/minutes/hours/days.