I am looking at removing an interior wall between my kitchen and living room and installing an archway in its place. It is not a load bearing wall. Is this difficult to do? How would I go about starting?

its not very difficult but not easier either, first you'll need a miter saw to cut the 2x4s , you'll also need a jigsaw to cut the arch out of the plywood, either hammer and nails , or screws and a drill.
1 1/4 sheetrock screws to attach the sheetrock
framing nails 12d will be fine
liquid nails to attach the arch to the ceiling along with nailing into the joist where possible

you also need sheetrock supplies as far as knives, mud pan, tape, screws, flexible corner bead

first thing to do is find out how long the arch is, once you done this take a piece of plywood, osb, whatever you want, and 1/2 thickness is fine,
once you find the length, find the center and make a center line up say 1ft or so, now decide how much of an arch you want, the one in my house I built was an 8", you can do the same or 6", if you go less, its just not much of an arch and if you do more you most likley need to make the plywood arch wider so you have enough left at the top of the arch, on mine I have roughly 8" left from the ceiling down to the highest part of the arch

so what you can try to do is rip a piece of plywood 16" find the center, measure up 6 or 8"
now you need to rip you something you can bend to draw your arch out on the plywood.
it want be a true arch so you want be able to a dowel rod and pencil method. what id try is take some 1/4 ply and rip and 1" or 1 1/2" rip and use this to bend and make your mark

the way to do this is to drive a nail into the center of arch at the 6" or 8" mark, now on both ends just drive another nail on each side to hold the plywood where you want it. trace this out and cut with a jig saw. now make another just like it.

once both are cut out you need to measure the wall in the house to match the thickness
keep in mind the plywood arch is a total of 1" the dry wall is also 1" subtract this off your exising wall and this is what you need to cut the 2x4s in between the plywood arches
as far as how many to cut, the more the better. on the bottom side of the arch place the blocks about 2" apart, you need a lot to screw the sheetrock to once you attach the sheetrock to the underside of the arch.

once the arch is built slide it into place and attach with screws or nails, 3" screws work best in case you have to take it back down. As far as attaching it to the ceiling try and hit the ceiling joist, if the joist are going in the same direction there may not be any to nail to. So what I've done is use liquid nails to help with this. You can still attach the arh on each end, which is fine.

after its up apply the sheerock and the tape and mud. Sand , paint