Can make anything from 40-80 grain bullets jhp or soft tip.
500 62 grain jhp using wheel weights and spent 22lr cases
From left: 22lr case, .224 jacket. Lead core, finished swage bullet, factory bullet.
You need:
Dies
This part costs the most money
there are a couple ways to get dies
You can make them if you have a machine shop and patience
You can buy them from a dentist that makes them part time. Mr Blackmon, a quick search here will turn up results on how to contact him http://castboolits.gunloads.com
You can buy them from a guy that makes them for a living Corbin. link to the Kit:
Corbin Swage Dies
I chose the 3rd route. $783.00+ S&H. Corbin also has several books he offers as free PDFs that you can read to find out more about swaging.
1lb Hard Rubber or wooden mallet
Reloading press
I used my RCBS AmmoMaster but from my research any heavy duty press will work the RCBS Rockchucker is a low cost favorite.
Warning: You are applying a lot of pressure and you may break your press. Must be a single stage press that uses standard dies or a swaging press.
22LR spent cases
You pick these up off the ground anywhere guns are shot. I sorted by brand so that the material and weight would be uniform. The batch I made used federal cases I still have a coffee can or 3 full of them from various manufacturers.
Step One: pick up and sort
Step Two: wash, I used an old pot that i don't cook food in and boiled them with dish detergent and vinegar a couple of times while stirring occasionally, then rinsing and drying on an old towel a few days, you want them to be as dry as you can.
Lead
I acquired mine from melting wheel weights I got free from tire shops, I already had a casting pot.
I used a core mold to make my cores. The core mold comes in the Corbin kit. Took about 2 hours to cast over 500 cores this includes initial setup and learning how to use the core mold that I had never touched before that night. You cast your cores with higher temperatures than you would casting regular bullets otherwise you get poor fill. I did not have to let the mold cool off the entire session because of the design.
You can order lead wire in .185 diameter and just cut the wire to length based on what weight you need. You can option to get a cutter instead of a core mold in the Corbin kit.
You make the cores to be the weight of the bullet minus the weight of the 22lr case. 55grain bullet = 10.3grain case + 44.7 grain lead core
Lead is known by the state of California to cause cancer and has been banned from being used as wheel weights.
I get my lead levels checked yearly for safety.
Making the jackets
Using the clean 22lr spent cases
I sprayed my cases with cheap silicon spray from the parts store because it was cheap and easy and covered uniformly. The cases get pushed all the way through the top of the die so i cut a hole in a butter dish to catch them and used the die to hold it while I worked. there is a sweet spot on where to set the die that makes this easier. but this is still the most labor intensive and the most likely to break your press because of the pressures required to reshape the cases into smooth bullet jackets. After you do this wash the cases again to remove the oil.
Annealing the jackets
If you have a self cleaning oven or propane grill this part is easy. put them on a cookie sheet that you won't cook on again and bake until they become red hot. If you do not have such modern technology or a wife that is understanding, you use a propane torch like I did. You might want to do this outside it smells. use the torch to heat the cases until they glow red, try to heat as evenly as possible.
Stick the core into your new jackets
Wash both the jackets and cores. I used degreaser but dish detergent should work. You don't want oil or junk between the lead and jacket.
I used a reloading tray that I made by drilling holes in a board to hold the jackets with the cores in them so they wouldn't fall all over.
Seat the cores
In the Corbin kit there is a bottle of anhydrous lanolin swage lube (you can make this with recipes found on the internet)
rub a little bit on thumb and 2 first fingers, not a lot a little goes a long way. rub some on the outside of the jacket, It should be coated but not too much. With the opening facing down onto the shaft and move the future core into the die. If your die is set correctly when you move the ram down the core will be stuck in the hole. Now take the hammer and briskly smack the plunger, this may take a couple of hits but don't swing like you are Thor, things will bend and break. Catch the new core with your hand and pile in an empty tray.
Forming the point
With lube in the same place as before, you want to place to push the core into the die with the opening facing up. Initially adjusting until you find the size of opening that you are happy with, too far and you will break your dies and spend lots of money. ( I did this
) not enough and the bullet will get stuck and is a pain to remove 
. Follow the how to set your die directions that come with the dies it will make life better. If your die is set correctly when you move the ram down the core will be stuck in the hole. Now take the hammer and briskly smack the plunger I used string and tape to keep it from flying out of the die because it is spring loaded, this may take a couple of hits but don't swing like you are Thor, things will bend and break. Catch the new bullet with your hand and pile in an empty tray.
Reload using what you find is the best load.
edit: clarification
