I'm swaging bullets the same way Fred is. Here's an example of how I make .357 bullets out of .380 auto cases. I'm using CH dies bought at
www.CH4D.com on a Rockchucker press.
I use SportFlite dies on my Rockchucker to make .22 bullets.
Then, 9mm cases to make .40 caliber bullets, and .40 cases to make 44 magnum bullets.
I've even made bullets out of .223 cases that I cut in half. Want to buy/make a .35 Whelen just so I can shoot the .35 caliber rifle bullets I've made!
In any case, there's just a few basic processes to complete, how you prepare your brass jackets, and how you prepare your lead cores.
Typically, I anneal brass on the kitchen stove till it's dull red in dim light. I might want to try leaving a can full of cases in the woodstove some time. As long as you can get them to about 700-800 degrees F they'll be soft enough to swage. If you noticed, .380 brass has a diameter of about .372-.374". After annealing I size it down to .356 in my Lyman lubesizer, then swage it back up to .357" in the CH swaging die. In general, you want to always increase the diameter of the finished bullet, not decrease it.
I've made cores four ways. I have cast lead cores (pic #1), cut lead wire (pic #2), and cast bullets in pure lead to make cores. I've also dipped empty cases into molten lead to fill and set aside to solidify. That gives you an annealed case and bonded core in one step.
Hope you have fun. If you already have a compound linkage press like a Rockchucker or something similar, all you need is a die set, which you can get from CH for ~135$. Remember though to go slow. I broke a Rockchucker in half by being too hefty on the lever.
Try to find one of the older editions of "ABCs of Reloading" by Dean Grennell. He always had a chapter or two dedicated specifically to swaging. That's how I learned how to do it.
Good luck,
Michael