To be wave soldering you're talking volume board soldering, not a few protos.
A wave soldering machine has a molten bath of solder, this will have typically two heaters, or more, tubular heaters immersed in it, (a bit like oven grill elements, but obviously with the end terminations above the solder level. You need two heaters - if you have only one and in fails, you are left with it embedded in a solid block!
The wave (or sometimes two) is raised by solder pumped through a channel just under the surface in the bath level. The pump is a screw type driven by a variable speed motor (to set the wave height). Obviously it's hell on bearings etc as they are running at molten solder temperature! The pump body is part of the tank so is heated at the same time and is of course not started until all the solder in the bath is molten.
Yes the conveyor is normally chain drive, moving reasonably quickly over the wave(s). Flux is applied (brush or spray) before passing over the wave. Everything is fairly critical - the solder bath needs to be big enough that the level doesn't drop too quickly as solder is used by the boards, doesn't get cooled significantly by the passage of the boards and doesn't suffer too much contamination. The wave height is critical, it must completely contact the bottom of the board but if solder runs onto the top of the boards they're scrap.
This all sounds impractical for diy. The bath takes a long time to heat at each startup (normally kept molten) and you then need to run a large batch of boards to make it worthwhile.
Your only hope might be 'dip soldering' where you hand flux the then dip the board onto the surface of a shallow solder bath - something like a solder pot, but of course big enough for the surface area of the board. You could maybe construct something like that with an external heater on the bottom, but even for something small you would need a fair volume of solder - enough to cause you a significant burn hazard in an accidental spill (think deep fat fryer but with 'oil' as thermally conductive as metal!).