The easiest way to work on the bike is to flip it upside down as long as doing so will not crimp your brake or derailleur cables or damage your saddle. Even a loaded touring bike can be flipped.
Remember to loosen the brakes before flipping the bike or attempting to remove the wheel. Flip the brake release or take the “noodle” apart.
If your bike does not have quick release hubs, be sure to carry a wrench capable of removing the axle nuts ( 14 mm front, 15 mm rear)
Shift gears to put the chain on the rear cog which is farthest away from the wheel (high gear). This makes the wheel removal and installation much easier.
Use proper tire levers to remove the tire.
Look for the reason your tire went flat – a wire or piece of glass is the most likely cause.
Once the tube has been removed, find the hole and check the corresponding spot on the tire to remove the wire or glass if present. If you see two small side by side punctures on the tube you have probably ridden the tire while it was under inflated, causing a typical “snake bite” puncture. If the puncture is located on the inside of the tube, check for a protruding spoke or missing or inadequate rim tape and remedy before reinstalling the tire.
Partly inflate the tube before attempting to install in the wheel. For the final push to get the wheel installed on the rim, you can remove most of the air to make things easier.
Do not use tools to install the tire on the rim. Roll it on using the palms of your hands. If your tires are particularly tight or you don’t have mechanics hands, carry a small tire seating tool or pry the tire on very carefully using the tire levers (only as a last ditch effort).
Be careful to not pinch the tube between the wheel and rim. Some soap or even water may make the tire bead pop on more easily.
Once the tube and tire have been installed on the rim, partly inflate the tube and check to be sure it is seated evenly around the rim. Failure to check this may result in the tire popping off the rim.
If you have tire clearance issues with your bike (fenders, large tires) you may have to inflate the tire after the wheel is installed on the bike,
If your brakes rub after the tire repair, check to be sure you have the wheel centered in the dropouts. The easiest way to do this is with the bike upright. Loosen the quick release slightly and you’ll feel the wheel drop into the slots.