Take a couple of tire levers (you can purchase these at your local bike/outdoor store). You can use the handle of a spoon or similar object if you don't have tire levers but be very careful, as you risk scratching or damaging the rims of the wheel and/or puncturing the inner tube. Ease one lever in under the wheel rim and lever out the edge of the tire (taking great care not to puncture the inner tube) and pry it up over the wheel rim. Move around the rim about a quarter of the circumference and repeat the process again, leaving the first tool in place. Now zip the second lever around the wheel and the tire should come right off on one side.
Either patch or replace the inner tube; or put on your new tire.
Check the tire wall for an arrow or similar to indicate the direction of rotation - some tires have a "direction specific" tread pattern.
Put one side in first, then ease the partially inflated tube into the tire and locate the valve in the hole in the rim.
Make sure that no part of the tube is sticking out.
Starting at the tire edge closest to the valve, use your thumbs to work the other side of tire over the rim and into well. You may need to use the same tool you took it off with to do the very last bit and pop it back onto the wheel.
Before inflating, use your thumbs again to ease the tire from the rim all around the circumference, peeking in to make sure that the tire is not pinching any part of the tube against the rim. When you inflate the tube, if it is pinching, it will pop, and you will have to repeat the entire process, and buy a new tube.
Inflate the tube slowly and carefully at first, all the time checking to make sure the tire is on evenly and there is no "pinching"
You're now ready to put the wheel back on the bike.
Happy bike riding!