Remove the wheel. With quick-release wheels, there should be a lever for this; otherwise you'll have to use a spanner. If removing the rear wheel, remember how the gears slot into the chain.

Remove the tyre using tyre levers. Wedge the levers between the tyre and the wheel rim, and try to pull the levers around the circumference while pulling the tyre over the rim. You may wish to inspect the tyre to make sure the cause of the puncture is not lodged in the tyre.

Remove the inner tube, remembering to unscrew the valve if necessary, and either get a new one or use a puncture repair kit. Inflate the tube very slightly, place into the tyre and press the valve through the hole in the wheel.

Use the tyre levers to put the tyre back on.

Screw the fastener onto the valve, then inflate to the correct pressure. The maximum pressure will be written on the side of the tyre. Higher pressure makes your bike go a little faster; lower pressure makes your bike a little more comfortable to ride on bumpy surfaces, but can increase the chance of a puncture if it's too low.