The following is the current method I use to produce very low cost jacketed bullets out of .22 rimfire range pick up brass and a lead core. A lot of people are familiar with cast bullets being made at home but this is a step up from that.
First I secure a good supply of rimfire brass and wash them with hot water and a drop of dishwasher soap, then sort by head stamp as I try to keep the variables down so I use one head stamp/make for one run since the point form die sometimes must be adjusted for that jacket in particular. The cases after they dry get derimmed in the .22lr jacket maker (no picture at this time sorry) and each one is examined for flaws. The brass then goes into a small toaster oven I drug out of the dumpster a while back to anneal. I leave them in until they take a very dirty brass color...these will now be suitable to form into bullets.
The next step is to find something to fill the jacket. I go with lead cast cores so that is what I'll cover here. These drop at .180" and will get formed in the first die of a 3 die set to create a very uniform core. Below we see the raw core not yet squished into a core ready to be seated.
Above core prior to being swaged for diameter and consistency, Below after core is run in die. Note flaws all removed and very sharp cylinder look.
So we have a formed core and a formed jacket lets put them together. This step is as involved as the individual chooses to make it. De-greasing the core and the jacket is one such step, Bonding the jacket and the core is another as well as adding any ballistic tips or partitions as one sees fit. Below we see the core simply dropped into the jacket (not yet upset) and the excess lead from the last step coming out of the side of the die.
Now we need to make the jacket and core upset to .224 and make sure the core is in the jacket in a uniform manner so it wont offer inconsistencies. Below we see the jacketed core exiting out of the die (picture removed for editing, I will have this back in sometime this week sorry). It is now a uniform .224", The core and the jacket are as smooshed together as they are going to get without the use of chemicals. Now the jacketed cores will go into a container being glass or plastic. After I am done with that run of cores they will get sprayed with a film of my own homemade lube of 99% alcohol and Lanolin and shaken to distribute evenly then allowed to dry. This is a very slick lube and is used prior to all the other steps (I don't use it to form the lead cores however. The jacketed core is set tip down into the die and the press is slowly but firmly manipulated. 
Above we see the finished product a short, large meplat 55gr bullet ready to be cleaned up and loaded. The last step I take is to dump bullets into a old t shirt put a small drop or two (for every 50 bullets) of Brasso and for 10 or so minutes polish them (by rocking the old shirt back and forth) so they are nice and shiny and all the lube and dirt is removed. Remember do not push these "free bullets" faster than 3,000 FPS or the thin jackets might come apart mid flight. The Corbin book claims 3,400 FPS but I have yet to try it. The thinner jackets and soft lead work very well on varmint but not on medium game. Bullets as large as .257" can be made with the rimfire jackets but they are lighter plinker bullets where as the RF jacket is the perfect length for a 55-62gr bullet. I figured that I need to make 8,000 of these free bullets to get the cost of the die set and press back but one should not look at the cost of the setup like that. Instead its a "give a man a fish, teach a man to fish" kind of thing. I'll never have to buy varmint bullets for my rifles ever again. And the joy of being able to supply myself with handfulls of these is tramendous.
