I got started by just changing the oil, after paying a mechanic to do it for 10 years! Then I just kept trying more and more complicated things. But I must admit, I was lucky enough to be working on cars not much more complicated than a bike - old Holdens - EKs, FBs, Toranas and Commodores. And now another oldie - the MQ Patrol. These days the computer and all the electronics would make it a bit more 'interesting'. But still a lot of things the home mechanic can maintain, and sometimes fix,on a newer car.
I found a couple of excellent text books that gave me a pretty good base to help think about how a car works. Its always good to know the 'big picture' before jumping in to fix or replace something.
There are some simple books in the shops, and then they range up to trade texts.
Have a look in shops that sell left over TAFE/Uni texts. I found a great technical college book on cars - design, function and service procedures. And from Repco I bought their Engine Service Manual. Its one of my 'little treasures'. Not sure if they still publish anything like that - mine is about 30 years old now.
At first you might make a few mistakes. But that's all part of the learning process.
One tip is not to get too keen on using all your muscle power to tighten up nuts and bolts. Especially with bolts going into, or through, cast aluminium/alloy components. You will either strip threads, snap off rusty bolts, leaving part of the bolt 'buried' in the bolt hole, or crack/snap/break the alloy part. Easy, common-sense general rule - the bigger it is, the more effort needed to both loosen and tighten. So be careful with the small ones!
Tightening up spark plugs in an aluminium cylinder head is a good example. If you strip the threads in the plug hole, then the whole head will need to come off to fix it. Very expensive learning mistake!
Get a feel for how much torque is required by loosening the bolt, or nut, just 1/4 of a turn, and then winding it back 1/4 turn to feel the torque. Don't be conned by the big effort required to break the rust/corrosion bond that might have built up since the last time it was removed. If you put that same 'oomph' in doing it back up you will be asking for trouble. As I said, 1/4 turn undoing it, and then stop, and 1/4 trun doing it up straight away to get the true torque feeling.
Of course a torque wrench and the car manual with the torque specifications is the way to go, but my torque wrench is only good for the larger nuts and bolts.
So start small. General maintenance to begin with - oil changes and oil filter, air filter, spark plugs, checking and topping up gear boxes and diffs, wiper blades, blown bulbs.
After that you could try radiator flushes, new fan belts, thermostat, water pump, starter motor when it 'goes west', same for alternator, shock absorbers.
But stay away from brakes and steering. Your'e not going to kill anyone if the motor stops, but brakes and steering - that's different!
And always talk it over with anyone who can give you a few tips of what to be careful of. Most people are happy to share their knowledge, provided you don't catch them at the wrong time!
Have fun with your big toy.