How do you hook up a hydraulic log splitter to your 1956 Ford 850 tractor?

PTO, hydraulics, or neitherThe first thing you need to know is whether the tractor has a PTO (Power Take-Off) or built-in hydraulics. Given the age of the tractor in question, likely it either has a PTO or neither.

If it has hydraulics, you should be able to attach the splitter. This may require the purchase and installation of a hydraulic transfer box. Be wary if you look at doing this yourself...hyrdaulics are fluids under high pressure and can cause devastating injuries when they leak.

If the tractor has a PTO, you can get PTO-powered hydraulic transfer boxes. From what I've seen they can be really expensive.

If you have neither, you're likely not going to be able to get this working.