Remove passenger side tire, upper strut mount bolts (the 3 in the engine bay), remove the lower ball joint (brake caliper and swaybar link removal are probalby a good idea somewhere in there).
After you have the axle somewhat free from the car (it will still be attatched to the chunk of suspension), you can HOPEFULLY just yank the axle out of the transmission... in the case you can not pull it out, you need to get the removal tool from somewhere...
After the axle is removed, unbolt the 4 diff cover bolts, remove diff, install new diff.... It is probably just easier for you to just see how it is assembled when you remove it for information on how to reinstall the new one.
You may want to pop the inner axle out of the trans on the other side, so the output shaft slides out with the diff. You can do the driver side axle pop without removing anything.