One of the most popular places for mods is nexusmods.com. They're so much easier to manage now than it used to be, too. When I started with Fallout 3, it was all manual installation. For the most part, you just download their Manager and you're good, though that doesn't apply to all mods. You have to read mod instructions carefully. Some will need you to alter a few things in your game-files but you usually just need to do that once and not for subsequent mods.
Read things like bug reports and be smart about conflicts. For instance, if you download two mods that alter the same thing, it's kind of logical that there might be a problem. I also recommend adding mods one at a time so if there is a crash, you can pin-point the cause.
That being said, games like Fallout and Skyrim are such known quantities now that most popular mods work well. On this PC, after hundreds of hours on Fallout 4, and with 98 installed mods, I've had maybe three crashes.
