How do you replace the rear struts on 2003 ford taurus...do they have ball joints in the rear?

No balljoints. Jack it up, unhook rear sway bar link from strut, unhook flexible hose bracket from strut, remove large bolt from bottom of strut, force rear wheel assembly down and off of strut assembly (some lube helps), that should be it for the bottom of the strut. The upper bolts are under the rear package tray, so you'll have to remove the rear seat and the package tray, remove the nuts, go back outside, slide out the strut and reverse the procedure with the new assembly.

that is a pretty accurate answer, so just confirming the top...

Dave's answer is correct. It is that simple.