Is it a hard process — like would I have to take it in to a shop to have it done — or could I do it at home?
depends a lot on motorcycle and if tubeless tire. I used to do tube type tire myself on /2 BMW's and Harley 16 inch, no big deal with tire irons. A size bigger or smaller was no problem- /2 wheel took from 3.25x18 continentals to the 4.10x18 Avon's. The Harley got 5.00x16 to 5.25x18 lower profile. Tubeless tires I get to shop with higher pressure equipment available. Rim width and type partial determines width of tire that can be put on, clearance on cycle when mounted is other factor. Lots of dirt bikes have clearance and strong rims for using full knobbies, block tread trial or chevron desert drag tires - and motards fit fairly fat track racing tires. If you've changed tires at home before, shouldn't be problem-- since you're asking here, suggest a shop. .
You aren't going to get a much wider or narrower tire on your bike rim. You might be able to go from a 180 width to a 190 width (common sport bike widths), but you will never fit a 200 or higher on the same bike. The rim will not support the tire and there will NOT be enough room between hard parts of the bike (like the frame and swingarm) for the tire. Go too small and the tire will not stay on the rim. Changing the rim is very expensive as no one makes them and you have to go to a custom builder and you run into the same problems with physical clearance on the bike.
It's not that hard to change a tire, as long as it fits the rim and has enough clearance to the swingarm, brakes, etc. But you won't be able to balance it properly. You could take it to the shop just for that
