Anyone that rides alone should know at least how to fix a flat tire. If you always ride with a group or you always ride with a partner, especially if your ride with a partner that is very mechanical you may be able to get by without this knowledge. You should still know how to check the tire pressure and what it should be. Most of the time you will find the recommended tire pressure right on the side of the tire. Check the tire pressure with a tire pressure gauge, not by the feel of the tire. Some tubes have Presta Valves, some have Schrader Valves, and make sure you know which one you have.
You can purchase at most bike shops and at most online bike stores, and Performance Bike a small device that pumps up bike tires using a CO2 cylinder. These take a while to get used to using, so buy some extra cartridges, you are very likely to drain the first few without getting anything in the tire itself.
It is best if you always carry an extra tube, or at the very least a patch kit. I have found that patching a Mountain Bike Tube seems to work, patching a road bike tube appears to be an exercise in futility. Your best bet if you ride a road bike is to carry an extra tube, and unless you are very good with the CO2 inflator, get a frame pump. I have had to carry my road bike for a few miles one time and now I always carry a new tube.
Here’s something no one ever tells you that could save you a real headache. In order to replace the tube you need to take the old tube out of the tire and after you do check the tire itself by running something along the inside. If you feel anything check to make sure it is not the cause of the blowout, glass or a tack can get stuck in the tire, if you put the new tube in a tire that has some sort of foreign object going through it then the new tube will get flattened also.
Also before you put the new tube in, blow it up and make sure there are no kinks. You don’t have to blow it up too much, just enough to get the kinks out that are there from it being folded up in the box, or wrapped in a bag. Check also that the new tube has no leaks. I have had a few brand new tubes that had bad valves, or even holes in them. I have also had tubes literally explode after they were placed in the tire. The exploding tube can often be avoided by making sure the tube is not twisted inside the tire. The narrower tires that use the Presta Valve are the most likely to have the problem. Install them carefully and make sure that there are no foreign objects in your tire.
If you have quick release hubs on your bike then you won’t need any wrenches to remove the wheel from the bike. For most bikes you will need a wrench to remove the wheels from the bike itself. A set of tire removal tools are invaluable for changing a tube. I have one that I bought in Arizona back about 20 years ago. It does not need to be fancy, the best one I have looks like a plastic screwdriver with a strange head on it. I also have some Maxxis Tools that my grandson Jason won at McDonough Georgia at a BMX Race. He picked up some Maxxis tires that day too.
Once you have replaced the tube and repaired the flat and have put the tire back on the bike you should check the wheel for True. That simply means that when you spin the wheel does it wobble back and forth or does the brake pads or the fork stay the same distance from the side of the tire all the way around?
Some of the causes of wobble can be a broken or weak spoke. It also can be that the tire is not centered or that the quick release has not been tightened properly. You can ride a bike for a while with a wheel that is out of true, but you should have it checked and repaired at a shop very soon after finding the problem. If you have a broken spoke or a bent spoke, you should have the bike checked by a competent shop ASAP. If it is a matter of the wheel is incorrectly seated or the quick release not being tightened simply re-seat the wheel or tighten the quick release.