Removing the front wheel - Release the brake cable at the brake. This allows the brake to open as fully as possible for easy wheel removal. Release the Quick Release Lever and unwind the lever a few turns.
Removing the Rear Wheel - Lift the back wheel off the ground while turning the pedals and shift into the lowest gears (the smallest cog on the rear wheel). If you do not have a work stand available, turn the bicycle upside down and rest it on the seat and handlebars. Use your hand to pull the rear derailleur out of the way and pull the wheel out, making that the chain is off the rear cogs.
Removing the Tire - First, make sure the inner-tube is fully deflated. Using your thumbs, push the tire away from the rim and insert tire levers. Pop one-side of the tire only off the rim and expose the innertube.
Repairing the Tube - Pump up the inner-tube to medium press and pass is slowly in front of your face. You should be able to hear or feel the hissing of air out of the tube. Once you find the leak, deflate the inner-tube and prepare to patch it.
In general, there are two kinds of patch kits. Ones with separate glue and patches and glueless kits where the patches have the glue already on them. The area that is to be patched needs to be cleaned. If using the glue buff the area to be patched and apply the glue. Let the glue set for about 3-5 minutes. Peel the foil off the patch and apply. Let dry a couple of minutes and reinstall.