I go to the workshop thingy in the main steam program. I found some things like weather and water texture changes. It told me to subscribe to get the mod, but I subscribe and nothing downloads. Nothing changes on my mod list, not showing any new content. And none of the graphical changes are there in the game.

I looked all around on steam's workshop page but there's no actual download link for these mods. What am I doing wrong?

You start the official game launcher. If you use SKSE you'll need to start the original game launcher to install and update mods then quit when it finishes and use the SKSE_loader program to actually play the game.