Someone should really write a guide for doing that, i'd love to play heavily modded skyrim but its so intimidating to sort through all the mods and figure out which ones are the best/aren't broken/etc.
Its been ages since i've played it and i've been thinking about playing through it again.
There's not much to it. Download Nexus Mod Manager.
Find the mods you want.
Download the mods with the link to the mod manager.
Instal them from the manager. If the manager asks you if you want to overwrite files from another mod, tell it no.
Every 3 to 5 mods you install start up the game to make sure it doesn't crash. if it does crash on launch then uninstal mods 1 at a time and check until you find the one that crashes.
My mod order I usually go..
Environmental
Beauty/Hair
Weapons/Armor
Follower based
Game Changing. (Things like major changes to spellcasting / combat / realism, animations ect)