So you have discovered that you have a flat and that it is a small hole in your tube, usually created by either a piece of glass or a piece of metal. If it is small enough, like something this size or maybe even a little bit larger, you will be able to patch it so that you can still get to where you are going. You always want to make sure that you are carrying a patch kit with you, a pump and tire levers.
These would be the tire levers, the patch kit and the small pump so you will be able to repair your flat if you are not around a bike shop. Basically what you do is find the hole first by pumping up the tube.
So I have already found the hole and marked it with a grease pen just so that I can find it easily. Then you are going to take your patch kit, when all of the air is deflated from the tube. There are a couple of different things in here. There are a couple different patch kits. These are glue-less patch kits, so basically they use a very strong adhesive that is like a sticker. There is also glued patch kits, which basically you have to put glue on the tube and you have to wait about five minutes. This one is a much easier solution, especially if you are on the go. It also comes with a piece of Emory cloth; basically it is like a piece of sandpaper. What you are going to do is markup that area, so that it gets a lot of scratches in it so that the adhesive will adhere to the very slick tube.
Once you are done with that just clean it off a little bit and make sure that there is nothing left over so that the adhesive sticks well. Then you are going to take your patch, try not to get much grease on it, or dirt, so it will stick. Find your hole again; make sure it is right over the top of it. Put the patch right on top. Make sure that you go all the way around the edges of the circle or the square, whichever it is, just to make sure that it adheres to the tube very well. Once you see that it has kind of become part of the tube you can pump it up.
Now that you see that it is holding air you can put your tube back in your tire. And that is patching a tube.