Everyone should have at least basic mechanical knowlege, but the more advanced stuff is still fairly easy to learn too. Having had a quick flick through some of my workshop manuals, I'd say that a good 80% of car work can be done by anyone with the manual dexterity to cook a meal.

A woman called a mechanic for her car, which was rattling and backfiring. He listened for a second, took a hammer and hit the engine hard, once. It started purring like it was fresh from the factory. He turned to her and said "$100, please."
She said "$100 for one hit with a hammer!" He smiled and replied "The hit with the hammer is $10. Knowing where to hit is the other $90!"
An old sexist joke, sure, but one that makes the point. First, you study.

Some colleges do evening classes on motor maintenence, but you probably already have everything you need to learn - a car, the internet, and (hopefully) the Haynes or Chilton workshop manual for your particular vehicle. If you do not have the workshop manual, that is your first purchase. It will become your bible for how to do things.

Meanwhile, a quick google search will turn up a bunch of forums dedicated to your particular vehicle. Read them until you find the one with the biggest section on mechanical repairs and join it (I'd recommend a gender neutral user name). Follow the rules, ask questions, read carefully. The forum will become your bible on how to diagnose things. Some of the forum members will become firm friends, willing to drive over and help you out with a two person job.

Then start with a simple job. If your car is out of warranty, service it yourself. Doing an oil change is about as difficult as opening a jar of pickles. Replacing spark plugs about as hard as changing a lightbulb. Small things first, to get your confidence up and translate book learning to experience.

Always think about safety. If you are working under a car, you have a ton or so of metal ready to fall on you. The battery puts out enough power to zap you dead. Exhaust systems get hot enough to burn your fingers to the bone in seconds (this one from experience).
And don't mess with your brakes until you are confident you can do it right. That is one of the jobs that looks easy, but if not done in a scrupulously clean manner can kill both you and others.

Finally, a word about tools. Buy the ones you need for a particular job. Dollar store tools are pretty useless, no matter how tempting they look and how keen you are to get a big toolkit. Some of my mechanics tools are nearly 100 years old, many are from WW2 (I inherited them). Buy good quality, as you need them. Look after them and they will look after you.

Good luck - it is a lot of hot, sweaty, dirty fun being able to repair cars. Take it as far as you like, from keeping your car on the road to building hotrods from scrap cars.