Don't know how to work on your car? Start learning ASAP.
The cost of a basic car repair is insane, and most is associated with labor costs versus parts. Yes, some parts do jack up the total for a car repair, but the true part of a repair charge is not the components. It's the work and time put into the repair, and in many cases you can do the work yourself.

Basic Filter and Oil Changes
Your car filters are in three types: general air flow, cabin filter if it applies, and your oil filter. Two for sure can be replaced by you any time. All you need to do is go to an auto store or check online for the exact filter model for your car, and then go pick it up. Engine air filters are extremely easy. You just pop the hood, find the filter box, open it up, pull the old one out, vacuum leftovers, put the new one in, close it up. Done. Cabin filters are a little harder and are usually located in the passenger foot well (check your car model). These might need a bit of body-twisting to get too, but removing and replacing tends to be easy. At most, you might need a Phillips screwdriver to open the filter holder. Probably, at best, a 20 minute job.
Changing your engine oil is a bit more complicated, but you can do every other oil change yourself. Most engine oil filters should be changed at a max, every 7,000 to 10,000 miles. But your oil changes every 5,000 to 7,000 miles. So, you can save yourself money by simply draining the old oil yourself every other change and keep your car running with clean lubrication. Just make sure to understand while plug underneath is the engine oil versus transmission oil (a very common mistake). Your engine oil drain pan plug is going to be further up towards the front wheels close to under the engine. The transmission oil pan drain plug tends to be further back and easier to see. On trucks, you make need to remove the rock shield first to access your engine oil plug. Simply have a good catch pan underneath, use a socket wrench or crescent wrench to loosen the plug. Remove the last twists with your hand so you don't lose it, and let the engine oil drain into the pan. Keep in mind, most cars will drain a couple gallons out, so you might want two drain pans at the ready to take it all. Once emptied, clean up, put the drain plug back in, tighten with your hand, and then gently tighten it finger-tight for a finishing seal. Don't over-tighten it! Then, back up top, open your engine oil entry valve or opening, pour in new engine oil to replace what you drained. Make sure the drain plug is in first or it will all go out again on the floor! Keep pouring until you have replaced roughly what you removed. You can use the engine oil dipstick to get an idea what is still needed. Don't over-fill! Put the oil in, run the engine, re-check when warm and top off. Done. If you can get to the oil filter when the old oil is drained, even better, replaced that yourself too, but remember you will need a special wrench to remove. Oil filters cannot be re-used. They are cheap; replace them.
Suspension
Replacing the rear suspension is extremely easy but does take time and manual work. You need a good set of socket wrenches and crescent wrenches for the job, a car jack, and hand gloves to protect your fingers. You can loosen but don't remove the securing nuts for the rear suspension where it connects to the frame and wheel axle. When ready, jack the vehicle frame up to carry the weight of the car when removing the suspension, otherwise you can't do the job. You might need two car jacks, and I use car stands in addition just to be double-safe if one of the jacks gives out. With the car propped and the nuts loose, you can now work on removing the old damper off the rear. Check the connections points and hardware, clean up or replace hardware if needed, and install the new dampner. Take your time securing the top nut first because this is the hardest to get access too and tighten. It's usually easier to remove the wheel to get at it. Once done on top, secure the bottom part of the dampner. Double-check everything is attached. Re-install your wheel if you need to. Make sure it is inflated. Remove the car stands if you used them. Then remove the car jacks one at a time. Make sure you are clear when the last jack is released. You have now replaced your rear suspension.
Front suspension works in a similar fashion, but they are called struts instead. Most now are a full assembly, and they attach as a complete unit. You have to go through a similar process like above, but it's more involved so removal of the front wheel is a must. Again, two car jacks and car stands are your friends here for safety. If you're good with manual tools, your biggest hassle will really be getting your car wheels off due to over-tightened lug nuts than anything else. Go slow and methodical, double-check everything, and you will replace your struts, saving hundreds of dollars in labor.
Replacing Your Car Battery
Car power struggling to start? Your battery is likely old. Even the best ones last maybe two or three years now before going bad. Most average batteries last 1 to 2 years. With the car turned off and the hood up, disconnect your black terminal clamp first going to ground (negative). Push it back and clear so it won't flop forward. Then disconnect your red terminal (positive). Push that out of the way. Unsecure the battery, don't lose the securing hardware, and lift and remove the old battery. Clean the battery bed area, and repaint if necessary (acid burns from the battery can cause minor corrosion). Place the new battery in the bed and secure it first with the stabilization bracket you loosened earlier. Then re-attach the red terminal first (positive), tighten, and next re-attach the black ground terminal second (negative), tighten. You'll know it's working when the black connects because the car alarm will go off with lots of beeping. Double-check everything is done, the battery is tight and in place, and the terminal covers are put back on (the colored rubber covers). Close the hood and turn on the car to check it's working right. You may need to reset your vehicle clock etc. Boom, you just saved yourself two hours of labor costs.
Got a Engine Check Light?
If you engine check light goes on, what do you do? If your answer is immediately go straight to a mechanic, you may not need to. In fact, your first step is really to park somewhere safe and then run a scanner to know why the light is going on. Your car has a computer which sends out messages in codes when something isn't working right. But for most, that is only seen as a check engine light.

I use an older Autel OBDII scanner. The newer ones have more detail, and these things are great, affordable, and easy to use. Anyone can operate one quickly. I put one in every car I have similar to a first-aid kit. You can get them online here.
With a hand-held OBDII scanner, you can plug it into the scanner socket underneath the driver's wheel, scan the car computer and find out the actual code. Some codes, like an oxygen sensor going bad, aren't immediate for going to the mechanic immediately. Your car may run rough, but you have time. Others, like a bad spark plug, should be handled as soon as possible to avoid engine or serious part damage. Without knowing, you may be spending a lot of money on unknown mechanics in a weird place when you could drive home and get to the service you know.
Other Options
An assortment of other issues can be taken care of with your car, again avoiding the costs of professional mechanical labor. And it will help you understand your car better when there is a problem that does need serious help. Everything from replacing burnt light bulbs to fixing wonky head visors can be done with a bit of learning and elbow grease. While they do great work, car mechanics do not require a rocket science degree to do their job. That means, the average person can learn the same skills too. Granted, you don't have all their tools and garage bay to work in, but you can do a lot of things that avoid expensive labor costs. This is why the neighbor down the street where you grew up was always working on his car on Saturdays. Now it's your turn.