tire off... caliper off... rotor off... axle nut off... remove the 3 bolts from the back of the hub (1/2" 12pt) then you can use a puller to remove the old hub.... but NEVER use a puller to remove a hub that you intend on putting back... if the hub pulls apart, then you must use this method (which is also the method for removing a good hub that you intend on putting back): remove tire, caliper, and rotor... back out, but do not remove, the 3 1/2" 12pt bolts that hold the hub in place about a quarter inch... use a center punch or an old socket to hammer the bolts inward until the hub cracks loose... you will have to turn the steering to reach all bolts... repeat hammering them until the hub comes free... you may have to use a wedge style tool to hit in between the hub and knuckle to help shock the mated surfaces while removing...
before putting it back on... grease the splines of the shaft and hub so it is a little easier to work with....
since you will have the hub off... pull the axle out (no extra steps, it just pulls out) and replace the Ujoint on it.... down the road, you'll be happy you did...
and yeah... the axle is mated with the hub, if the bearing is bad, and it can shake, the axle will move with it