Many people look to save money and repair their cars themselves. Not that there is anything wrong with this. You just need some patience, some tools, and some time. A digital camera would also be a good idea as well. Also you might want to look into a repair manual if it gets really involved. These can give torque specification and if certain parts need to be changed.
Starting off I would not go to big. Keep the repairs simple, oil changes and air filters. These can make a big difference in the performance and gas mileage of any vehicle. Think of it like this, if the oil is dirty it will not lube the engine enough and cause some unneeded heat. This will cause the engine to work a little harder to keep itself cool. An air filter can restrict the air flow to an engine. Try to put your hand over your mouth and open your fingers a bit. You have to work a little to get air, same thing applies here. One more thing, check your tire pressure. They say for every 2 psi under inflated your tires are you lose 1 mile per gallon. Those are simple enough. Always check your vehicle owners handbook for any placement locations. Also for your oil amounts, air filter recommendations, and tire pressures.
Now if you are going to go deeper with a repair, a digital camera would be good to have. As you take apart you vehicle, you might lose track of where things go. The pictures can remind you where parts go and which bolts to use. This can also be good, when your waiting for parts. You can put bolts in a small zip lock bag and label what they are. Go slow, especially if it is your first time. No need to break or cause anymore damage that is already there. Look at how the thing you trying to remove come off. There might be a seal that needs to be fit just right when going back together, if not fit right it could cause more problems. I have worked on cars for years. I still did this every time. After a few times doing the same repair, I am sure what needs to go where.
Do not over tighten things. Manufactures make torque specifications for a reason. Torque is defined by Webster as: A turning or twisting force. When you over tighten things, you could be causing more damage making a repair take longer. You can warp parts easy, especially when they are aluminum. You can also destroy gaskets and seals. Always put bolts on by hand first, if it is not going in there is a reason. Figure it out, move stuff around. Sometimes if your changing a part, the weight of a part can make bolts feel tight. Move the part around a bit to see if the bolt is easier to start threading. Remember take your time when doing a repair.