Fallout 4 mods are on Xbox One today, May 31. They'll be on PlayStation 4 "next month." Technically, tomorrow is next month, but Microsoft pulled some strings to get a timed exclusive, so it could be another two or three weeks for PlayStation owners.
Here's an in-house video from developer Bethesda about the mods you'll be finding on console. Which is crazy in and of itself. Mods on console, people. That's never been done before.
The main menu injects the new mods menu right into the middle. Link your Bethesda.net account to your console, then you'll see a bunch of thumbnail images appear in My Library.
You can browse mods online at mods.bethesda.net, or browse them in game. Categorical breakdowns divide buildings, folliage, characters, top downloads, etc. You can download a maximum of 2GB worth of downloads for now. You can't just download all the mods. So there's the 2GB ceiling. Bethesda may up that limit in the future, but you'll have to chill for now.
The game maintains your unmodded saves, then starts a new branch of saves once you activate any mods. It will say [Modded] in the save file name. Also, not because mods are cheats, per se, but Sony and Microsoft require Trophies and Achievements to be disabled once you start putting mods iton your game. Keep that in mind if you're an achievement hunter.
For a few examples of what you can download and start using right away—even in a brand new game with a brand new character—go to the 14:15 mark in the video where you'll see that they turned Dogmeat into Catmeat. 14:35 shows off a Nuka Cola red Pip-Boy on your wrist—which happens to do a bunch of other crazy stuff, like giving you all weapons (watch your encumbrance!), revealing every location on the map, jumping 3x your usual jump height, and a ton more.
If you want to make mods, you have to have the PC version, downloading the free Fallout 4 Creation Kit. Then, after making them on PC, they can be pushed to Xbox One and PlayStation 4.
Making mods isn't easy. It's work. So don't yell at modders, saying, "I want this, make it for me, plz," and then expect it to magically appear in 30 minutes. This ain't Mario Maker. It'll take more time than that.
We gave Fallout 4 our highest score, and the Season Pass content—Automatron, Wasteland Workshop, and Far Harbor (review soon)—has all been great. Everytime I think I'm free of Fallout 4, it sucks me back in. I'm guessing you've had the same problem.
Again, Fallout 4 mods are out for Xbox One now, May 31, and "next month" for PlayStation 4.