There isn't really an "easy" way to play modded Skyrim unless you use only a few mods. You usually have to mess with load order, test mods one by one if something breaks, read mod description for potential conflicts with other mods and important notes, find whatever conflicts etc. There is lots of tutorials for mod organizers which help a lot and just reading mod descriptions pretty much eliminates the most common problems but sometimes conflicts aren't known and you find them randomly.
Skyrim Special Edition is pretty stable compared to normal Skyrim even with mods. I had hundreds of mods on it before I quit for a bit due to space and time to keep adding mods to play with no issues besides one load order issue I had to fix. That's all pretty much the basics until you get too many and have to mess with other things if you hit the 255 mod limit for esp/esm/plugins.