"I just find a socket that will just slip through the new bearing. Then I hang the old unit in the vise, with the hub hanging down. Then I tap it out using the socket."
I just did it that way for the 5,000,000th time on Tuesday. (A rough estimate) Among those past removals, I only had to torch off one throwout bearing that absolutely wouldn't budge. The rest tapped out easily with a good-sized hammer. The suggested tools above are neat to have handy, but this method works 99.9999% of the time and costs nothing. You just need a well-mounted vise on your work bench.
To install the new bearing, orient it so that the broad flat side lies against the closed vise jaws, set the bearing carrier inside the bearing - being sure it's straight - and then place a short piece of 2" x 4" wood across the carrier's top. Hammer on that to drive the carrier into the throwout bearing until it seats. Resist the temptation of hammering directly on the flange of the carrier. That will distort the edge and compromise the carrier's round shape, making it hard to slip the carrier over the transmission front bearing retainer snout.
Marshall