Fixing a tire with a nail in it is something that everybody should be able to do. Bike tires are not indestructible. You might be surprised to learn that fixing a tire with a nail in it is actual preferable to having to fix a tire with a small leak. This is true because finding the hole can be very difficult when you have a slow leak as the hole can be very small. When a nail is sticking out of your tire, you know where the hole is.
You will need a few tools to repair your flat tire. It is a good idea to keep a patch repair kit on you if you are riding long distances or in remote areas. Your kit should include a small air pump to refill the tire once you've patched it, a set of tire levers (or "tire irons"), a patch kit, a spare tube and a wrench that fits the axle nuts.
The first thing you need to do is flip the bike over and lay it upside down, balancing on the seat and handle bars. Spin the tire so the nail is sticking up toward you. Use the tire levers to pry the tire off the rim. Next you will pull the tube out, being careful to keep tabs on where the nail's puncture is. The nail will no longer be marking where the hole is as it should have come out when you pulled the tire off the rim.
Now you need to patch the tube. You need to make sure the tube is dry as the glue won't work if the tube is wet. If you're caught out in the rain, carry the bike to an area that is protected from the rain before prying the tire off. There is a small tool in a patch kit that is used to scuff the tube. Rub the tube with the tool and make sure the area around the hole is no longer smooth. The glue will not bond well to smooth surfaces. You should also make sure to brush any dust off the area as it will compromise the effectiveness of the glue as well.
Squeeze some glue over the hole and an area a little wider than the patch. Peel the backing paper off of the patch and place the patch over the glue. Push down hard to ensure a good bond is made between the tube and the patch. You can use the tire levers to squeeze the area if you don't feel you can squeeze hard enough with your fingers.
Once the glue is dry, you can place the tube back on the rim. Also, make sure you pull out the nail before replacing the tire. Using the tire levers replace the now nail-free tire. Refill the tire using the air pump and continue on with your ride.
The modern cycling training schedule does not require you to train year-round for any specific race.