Step 1: Get ya wheel off.
First things first: you need to remove the punctured wheel from the frame.
If it is a rear wheel puncture, change gears so that the chain is on the biggest chainring on the front and the smallest cog on the rear cassette. This makes rear wheel removal easier.
You'll need to disconnect the brakes: on road brakes, just push up the quick release on the side, or squeeze the callipers together and pull the noodle backwards to release the brake cable if you have cantilever or V-brakes. If you have disc brakes you don’t have to do anything more than open the quick release skewer or thru axle to remove the wheel from the frame.
Some commuter bikes uses wheel nuts - if this is the case, you'll need a spanner - often 15mm - to loosen these off before you can remove the wheel.
Step 2: Unscrew the valve cap and nut.
Take off the valve cap (the little piece of black plastic over the valve) and unscrew the valve retaining nut (the round ring siting against the rim) if there is one.
Push the end of the valve to fully deflate the tube if it's not already empty of air - this can sometimes be the case if you have a slow puncture and the thorn/ debris is keeping all the air from escaping.
Step 3: Use tyre levers to loosen the tyre
Check the outside of the tyre for any clear causes of the puncture. If you see any debris stuck in the outside of the rubber, remove it and make a mental note of where it is in relation to the valve.
Gently insert two tyre levers between the tyre and the wheel rim - do this one at a time, and make a gap by pushing the first tyre lever down 90 degrees, and you should be able to fit the second one in. Then with the tyre lever furthest away from you, hook it to the nearest spoke. With the other lever, pull it towards you so it is two or three spokes away from the first tyre lever. Now you can push down and it should pop the tyre off.
By now the tyre should be loose enough to simply run a tyre lever around the wheel rim to remove the rest of the tyre.
You can do this step with your hands, but be prepared for some bloody knuckles and profanity.
Step 4: Remove the tyre
Pull out the inner tube, removing at the valve last. Now, you've got two choices - mend the tube and replace it, or simply use a new one. It's usually easier to use a new tube out on the road, then mend the punctured one when you get home.
Step 5: Check the tyre for debris - IMPORTANT.
Examine the tyre around the outside for any debris. If you find something, remove it. If all clear, carefully run your fingers around the inside of the tyre to check there is nothing else penetrating the tyre - if you find anything (small pieces of glass, thorns, gravel), remove it.
Not doing so can result in the dreaded double puncture. No one wants a double puncture. Trust us.
Step 6: Refit the tyre on one side and insert the inner tube
Refit the tyre on one side. Make sure the tread is pointing the right way — some tyres have arrows on the sidewall indicating the ‘direction of travel’. Some tyres are bidirectional and can be fitted in any direction.
Put the valve in the valve hole, and feed the inner tube into the space between the tyre and the wheel rim.
Step 7: Refit the tyre completely
When the inner tube is all in, twist the tyre back into place, starting at the valve. Try to finish directly across from the valve as the tyre will be looser there, and use your wrists to roll the tyre on, as shown in the picture above. If it gets difficult, let a little air out of the inner tube. Check there are no bulges and that the tube isn't pinching under the tyre bead.
You can use tyre levers to help with the last section, where the tyre is tightest - but if possible avoid this as they can pinch the tube and cause you to have to start all over again.
The tougher and newer the tyre, the harder this will be - by contrast well used, supple summer tyres are usually much easier to get back on the rim.
Step 8: PUMP IT.
Get ready to get your sweat on and pump it! Aim to pump the tyre to the correct pressure (usually noted on the side of the tyre).
Once you've reached the correct pressure, tighten the valve back up and refit the wheel into the bike securely. Close the brake quick release lever or reattach the brake cable. If you have mended a rear wheel puncture, whack it back to an easier gear, do a little test ride, and go through the gears. Check that the wheel spins freely and the brakes work correctly.