For PVC extrusions, the process is the same as welding that pipe, Craig.
Welded PVC window frames are cut to a miter and usually slightly longer than the finished size intended. The pieces are clamped in a jig, a hot welding plate is placed between the miter and the pieces are heated. After reaching a melt temperature, the plate is withdrawn and the miter joint is pressed together and allowed to cool. The cooled weld joint is milled into tolerance to complete the process.
Check out this short video of a four point vinyl welder that welds two sash at one time. You'll see the heated plate at 1:00 minute with various closeups until 1:30. The heated plate is covered with a "teflon" style coating to keep the melted vinyl from clinging to the welding plate. The rest of the video is more window nerd stuff. :laughing:
Build your manual welder with something that has a low stick coating, say, a high temp silicone paint like what is used for coating cookware or bakeware. Also, a hot knife will let you heat the joint over a wider area. Heat, melt, separate, and press together until cool.