Firstly, make sure that it's not your valve that's leaking. The best way to test this is to immerse the valve in water. If you can see bubbles, that's the problem.
Repairing a puncture is easier at home than on the road, and you'll need the following tools and materials - tyre levers, a spanner, a puncture repair kit, a bike pump, a spare inner tube, and a bucket or bowl full of water.
Locate the puncture by rotating the wheel and checking for sharp objects, which must be removed. To repair the puncture, first remove the wheel by loosening the wheel nuts with a spanner, and if you have a modern bike, operate the quick release bolts or mechanisms on your brakes. Take the wheel off.
Check that the inner tube is deflated, push the side wall of the tyre away from the rim - this must be done on the opposite side to the value. Insert the flat end of a tyre lever into the gap, and push the lever down to hook over a spoke. Insert a second tyre lever next to the first and repeat the process. Place a third lever carefully under the tyre wall, and run it all the way round the tyre wall. One side of the tyre is now free, so you can reach in and pull out the inner tube a section at a time. Unscrew the valve and push it out carefully.
Give the inner tube two or three bursts of air with your bike pump. Place the tube in a bucket or bowl of water, and look for bubbles. Mark your puncture with a crayon. Take the sandpaper from the puncture repair kit, and roughen the surface of the inner tube. Apply the rubber solution and blow on it to speed up the drying process. Then chalk over the rubber solution to soak up any water, and place the patch over the rubber solution.
Check the inside of the tyre to see that it is clean and anything that may have caused the puncture is removed.
Carefully putting the valve back first, replace the inner tube. Pump it up gently and tuck it up against the rim all the way round the wheel.
Push the tyre wall up and back over the rim, starting at the valve. Check the valve is in the correct position, at right angles to the rim.
Pump up the tyre, re-connect the wheel, then the brakes, and check to see if your brakes are functioning properly. Your tyre should be firm, and you're now ready for that bike ride.