it depends on the car. the biggest problem I have had is lining parts up when reinserting the ball joint into the control arm (or whatever its called). sometimes I have needed a 2nd person. I've done it on: GM full-size cars, Dodge K variants, escort.
A rack is sure nice.
But you can do it at home, for sure.
To get the axle out of the tranny use two prybars or screwdrivers on opposite sides of the inner C/V joint, and quickly and forcibly pry/pop the joint out. Bigger bars are better. There is a circlip that holds it in position.
You may have to drain some lube out first, so it doesn't leak all over.
BTW, the axle socket will be tight. Unstake it or yank the cotter pin first! Impact tools are nice for this.