Some questions......does your bike's rear wheel use a quick release or bolt-on rear axle? Does your bike use a cassette or freewheel? While they may look a lot alike, they are completely different animals. How many speeds (gears) does your rear wheel have? How many does the one on craigslist have? Certain gear combos are not compatible with each other (cannot mix 9spd. stuff with 7spd stuff, etc.)
Are your wheels' rims steel or aluminum? Most steel rimmed wheels are much wider than aluminum rimmed wheels and won't fit the braking systems without either a lot of adjusting or completely changing them.
As for getting a cassette/freewheel off, they're very easy to get off and on, provided you have the proper tools.....cassette lockring tool, chainwhip and an adjustable wrench. Freewheels are about the same, but instead of using a chainwhip, I have found putting the freewheel tool into a vise and then putting the wheel onto the tool and unmounting the cluster the easiest way.....just unscrews off the wheel.
Just because both wheels are 26" diameter, doesn't mean they'll automatically fit any bike frame.......many other variables involved.