You need an allen key.
Some stems are front-loading, so you can leave brakes etc on you handlebars, but with most, you insert the bars from the side, so remove all grips and controls from your bars.

Loosen the stem within the fork:
Rotate the allen key on top of the stem no more than 2 rotations (If you turn more, the wedge at the bottom will fall out).
Tap the allen key gently with a piece of hardwood, to push the wedge down.
Turn the handlebars sideways, holding the front wheel.
The stem can just be wiggled out upwards.
Before you do this, tighten the allen bolt a little and loosen the bars in the stem.
Undo the clamping bolt and rotatate the bars a little. They may be stuck due to corrosion. Retighten, then remove bar and stem from the fork.

Be careful not to scratch the bars when you take the old stem off, or put the new one on. You may need to rotate the stem on the bars at corners.

When you put the new stem in, put a dab of grease/antisieze on all surfaces which touch metal. Smear a little grease along the central bolt and wedge to rustproof them.