You can "get the job done" with a 110V portable welder, such as the Lincoln "Weld-Pak" machines you see at Home depot, but it's much easier with a 220V MIG welder. The way that I do it is to stack up my billet(s) using an old milling machine vise (one of these days I'm going to build myself and air vise for this purpose), and then run a very shallow bead across the edges of the stack....one near what will be the front, another across the middle, one BOTH sides. I then set the billet up so that the end I will weld the handle on is facing up. I use old rebar for handles. I position the piece of rebar in the center of the end (the end that I did not run a weld bead across previously), then weld the handle to the billets, and run a bead from the handle to the outer edges of that end. The important part is that you want to make a SHALLOW bead... just enough weld penetration to hold everything together. I then do my first forge weld, and then I grind off ALL the weld beads on the EDGES. If you fail to do this, or miss some weld bead, it will end up in the finished billets as an "ugly grey glob". From there it's just a matter of continuing forge welding, restacking to achieve my desired number of layers, and any manipulations to achieve my end goal with the pattern.
There are some folks who still use the method of wiring a billet together, but compared to MIG or Stick welding the initial billet together, the wire is just a pain in the backside.