I did this job twice (both sides) about 2 years apart. I replaced the left side bearing because it was noisy and needed replacing. I did the right side because the "new" bearing had been in the freezer for 2 years by then (except for the days while we were moving
) and my wife started giving me attitude about it. (I just wanted to be sure it was really cold.)
Actually I had just bought an air-powered impact wrench, and liked using it, so I pulled the right side bearing for no better reason than that. In hindsight, probably a stupid idea. But it got the bearing out of the freezer.
My first generation made-up puller was loosely based on a large puller kit that I bought at a chain auto parts store, not sure what it was for except that it was American and not wheel bearings. Not even close to the elegance of the hardware-store puller described earlier in the thread. But it got the old bearing out, and the new one in. (I later had a machinist friend make me a couple of properly sized discs out of 1/2" thick aluminum to improve the puller for round 2. Then last month I used those discs to pull the rusted-on rear brake rotors off of my wife's Mercedes. But I digress.)
The first time, I retorqued the axle nut using a 30mm socket (I think that is right, for my car anyway) on a long ratchet (breaker bar would be more durable, probably). I put the 2 pieces of pipe that make up my jack handle together, and slid the big end (not the one that goes into the jack) over the ratchet handle. I divided the torque rating (converted to foot-pounds) by my body weight (less than it is now) to figure out the appropriate distance, then measured from the center and put a piece of tape on the jack handle, and stood on the tape and jumped a little until the nut stopped moving. I figured that I would break the ratchet, but it held, and that bearing has been perfect for 7 years.
The next time around I figured my (allegedly) 500 ft-lb impact wrench would get it tight enough, but the wrench is kind of a POS so I don't think it got the job done. That one has always been a little loose. I think I will have to go old school on that side too. Of course by now I may have toasted the new bearing by driving around with it "a little loose" for all this time.
I know that this sounds pretty barbaric, but during a Porsche engine rebuild school I attended years ago, I was told a possibly mythical story that real Porsche race team mechanics once used similar methods to get these nuts tight. The point being that there is not much risk of over-tightening and breaking something, because all of this stuff is hard to break.
YMMV. But it sure did work well the first time. And I also used the same technique on my old VW Golf, which was retired years later for other reasons. So I guess it worked well twice.
Scott