This seems like an interesting hobby. How much time is needed to achieve a reasonably high understanding of this work? Not industrial grade expert, but a knowledgeable layman. And where/how can I educate myself?
Then you need a project that you want to do and ask those guys how you can get there. You will need to learn some CAD, some mathematical concept and you will get something.
Then you print your pieces using their printers. If at this point you enjoy it, you will want to have your own 3d printer. The guys will help you with this too.
For example I am part of Clone Wars RepRap, an Spanish language group. We are more than 5000 people. We help each other a lot. I am also part of German,and Austrian groups.
Without the social environment, buying a printer yourself you will probably find it too hard, specially at first.
But if you want to buy one, you can find very nice 3D printers at $250 - $300 range from aliexpress etc. It may take hours, a day or a week for calibration (depending on your printer model and printed part quality expectations), and you are good to go.
But I must say that, 3D printers need maintenance and that can take your time as well.
If you want to educate yourself, http://reprap.org/ is the site you would want to visit. Not only for making your own printer, but calibrating and maintaining a bought 3D printer as well...
If you want to try your hand at 3d modelling then you'll probably download Sketchup as a start and noodle around while watching youtube tutorials on the side. In about 8h you'll feel confident enough to actually model something meaningful. After ~40h you'll be able to knock together a model quite proficiently.
After you'll have gotten tired of Skethub producing broken STLs and not allowing you to change your mind after modelling a thing, you'd move on to one of the real CAD software package, like Solidworks or Fusion 360 (which is great for beginners, btw). That rabbithole goes exactly as deep as you've got time for :)
Fiddling with the printing itself will take a bit of setup time before each print and then a lengthy wait (hours to days) to get the result, or see it fail in some new and unfunny way. It's not really all that difficult, to be honest, just takes some time to develop an intuition about what's likely to fail.