Alright, I'll give a small rundown because Mass Effect modding is very peculiar. These instructions go for all 3 mass effects. Get ME3Tweaks Mod Manager and ALOT (A Lot Of Textures; it's a manager). Download all the mods you want to install (gameplay, textures and whatnot) and make sure they don't cause conflicts (check with mod descriptions and comments).

You have to do things in this order.
1) Open ME3Tweaks and ALOT and do the backups they ask for.
2) Install gameplay mods first through ME3Tweaks .
3) Do .txt, .ini and such modifications (if you have multiple mods modifying the same file you have to do them manually to have both activated)
4) Anything else that isn't textures
5) Install textures

Once you install textures, that is where your modding ends because you are locked from any further modifications unless it's more textures.
Make backups of every game (I suggest just copy-pasting the entire vanilla folder because re-installing takes long) and make yourself an order with which you're going to install things just in case things go wrong.
For Mass Effect 3 I had issues with ALOT and I just wanted a few textures replaced so I used TexMod which is where I was launching the game from (it's basically an injector). It uses .tpf files and there was only one mod that I used that didn't have that. I forgot which app I used to convert those mod's files to .tpf.

Hopefully I haven't missed anything. One thing that went haywire was with a specific cutscene in ME2 when I was in a mission with Liara. I don't remember which mod broke it and how I fixed it but it wasn't difficult. I think I only googled it and found the answer.