Is it possible for a novice to take out an over-the-range microwave and install a new one, or does this need to be done by someone who knows what they are doing?

It always helps to know what you are doing! 90% of MWs are held up by 2 long screws that run through the uppur cabinet to the MW. Usually a 2 person job due to weight and bulk. Typically you will remove old one, install wall template, hang and bolt. Takes less than 1 hr in most cases.

I'm pretty sure you can do it, with help, it's definitely a two person job, three is better (two to hold the microwave, the other to pass the supplies over). :)

Just read the instructions carefully, follow them to the letter, and don't start until you have everything in place.