Mike is correct. The management part of rentals and the physical repair work are different.
To answer your question about repairs, personally, I grew up in a family who always did our own construction. Building houses, barns, warehouses, simple shade shelters for livestock, etc etc was just part of growing up for me. To be fair, like everyone, I have my strong and weak suites on repairs. For example, I'm a pretty good carpenter but I'm terrible at wiring.
I'm a big supporter of the best way to learn is to do mentality. If you know anyone in the construction business, even if its your cousins neighbors brother in law, hit them up about hanging out at the job site for a day. Just watch how they do things to begin with. Over time, you may be able to assist them with something.
If you prefer the classroom environment tons of Vo-Tech colleges/classes are available.
Just remember, like anything in life, skills aren't learned in a day. Be patient and know your limits. Changing something like a garbage disposal is a pretty good starting point. You probably shouldn't be ripping off shingles to replace roof decking as your first DIY job.