Shift your gears into the smallest sprocket (lowest gear) to create slack in the chain and make removal easier. Putting the gears onto the smallest sprocket also makes it easier to put the rear bike wheel back on, since you won't need to remember which gear you used when you last cycled.
Shift gears by lifting the bike by the seat and pedal by hand until the chain has reached the lowest gear.
Loosen the brake calipers to prevent the tire from bumping into the brake pads when you remove it. Side brakes can be opened by rotating the little brake lever upwards or by pressing a button on the lever. If there is no lever, hold the brake cable and push the arm in until the brake disconnects.
Loosen the nuts on the rear axle or pull down the quick-release lever. Pull the bike rear wheel out.