I'm a long winded SOB, but I'm going to challenge myself to make this short & sweet.
A loaded round is four components. Brass case, primer, powder, bullet.
At it's most simple, you take all your empties and you run them through a sizing die. The sizing die squeezes the brass back to "like new" shape and it also punches the old, dead primer out.
You then use a tool to put a new primer in each case.
Then you run the cases up in to a case mouth flaring die to "bell" the case mouth so it will easily accept a bullet without crushing or mashing anything.
Then you add the appropriate amount of powder. This is a real art and where you make either great ammo or atomic bombs. Every aspect of reloading takes care, patience and skill, but nowhere is it as important as when you charge the case with powder, for obvious reasons.
Then you set a bullet on top of that sized, primed, flared and charged case and you run it up in to another die that seats the bullet to the proper depth and puts a crimp on the case that either closes the flaring you did earlier or helps hold the bullet in place or does both.
Each of the steps takes time to setup properly, but you only have to set them up once. (well, you change seating depth as often as you change bullets...)
At it's bare bones basic, you need:
--one reloading press
--a priming tool
--one set of three dies for a handgun caliber (can get by with 2 dies for a bottle neck rifle caliber)
--a scale to accurately measure powder
--and a supply of those four components I mentioned above
There's a hundred more tools and goodies you can buy to make the process better or easier or just more enjoyable. Heck, there's a half dozen tools that you sure as hell should buy, but those things I listed would be enough to make it happen safely and would produce very good ammo if you did your part.
A good reloading manual will cost you anywhere from $15 to $50. Check your local library, you may be able to borrow one for free just to give yourself a taste. A manual will teach you how to do it, how to make sure you stay safe and why it all does what it does. A manual is an absolute must for a new reloader.
Some of us (not all of us) end up enjoying reloading as much/more as shooting. For me, if I lived in the sticks and could shoot whenever I want, I would still like shooting more. But because I have to plan the time to shoot, haul the gear, make the trip, etc etc, I end up enjoying reloading even more than shooting because it takes me only 10 seconds to go down to the man cave and work at the bench.