Tire tools are cheap and light. They're about the size and shape of toothbrush handle, and it's a good idea to carry a couple with you whenever you ride. They're easy to fit in a small pouch under your seat along with a spare tube, and with a frame-mounted pump, you're all set.
The first step is to take the wheel with the flat off your bike. Do this by loosening the nuts or quick release mechanism that holds the wheel until it slides out. You may need to loosen your brakes to get the wheel off. These often have a quick release mechanism too. If you are removing a rear wheel, it will also have to be lifted clear of the chain.