If your car has original axles it should be "one piece" axles.... you probably bought a reman that requires a core -- you won't be penalized if the core comes apart....
you'll need a 30mm axle nut to get the axle end nut off.... lift the car, remove the wheel, unbolt the two lower strut bolts, pull the hub towards you and to the right... push the axle end out of the hub (after you have removed the 30mm nut) and you should be able to just barely slide it out... pull (yanking) on the axle until it pops out... it only has a circlip holding it in place.... how easy or difficult it pops out depends on how wide the circlip was set..... it can be difficult and it may fall apart.... don't worry, just toss all parts into the box. If it comes apart, then use a prybar to pull the remaining stub shaft.
You will want to drain the trans prior to pulling the axle --- because if you don't, then it will drain the diff once the axle comes out. If it's an AT you'll have to pull the pan (get a new filter and seal) if it's an MT just pull the 24mm bolt at the very bottom of the transmission, facing the driver side. It's a large/flat bolt.
Install in the reverse. (FOR AN MT

Filling the trans can be done 2 ways... through the fill bolt on the middle of the trans facing the front of the car, or if you're good you can pull the speedo drive gear and fill the diff. You should need about 2.6-2.7 quarts total.