This seemingly daunting task can actually be accomplished with very little plumbing knowledge in just a few minutes (assuming you’ve got the necessary stuff ready).
All you need is the new toilet, plumber’s putty, teflon tape, a wax ring, and the necessary hoses (which should come with the toilet), and this video I’ve got below for you.
Remember to turn off the water to the toilet before doing this (obviously, but you’d be surprised how many people don’t do this and end up drenching themselves and their bathroom in the process), get some help moving the toilet(s) around (they’re porcelain and consequently very heavy, it’s very easy to throw your back out doing this–get help, trust me), and follow the instructions:
Additional Help and Tips
This is the best set of written instructions I could find online, it’s from This Old House plumber Richard Tretheway, and the pictures and detail they go into are excellent (note: the 4-6 hour time estimate they have includes buying supplies, once you’ve got everything you need it really shouldn’t take long).