I noticed on the Unique Player mod page that there were many comments about the mod not working.  The mod works, but there may be some steps you need to do to get it to work for you.

First you need CBBE and Bodyslide/Outfit Studio installed.

Next, download and install the Unique Player mod.

Finally, download and install this Unique Player Bods mod, it adds a few more unique player presets (I use the 3BBB preset).

Open Bodyslide, look in the bottom left corner next to the Batch Build button. Make sure that Build Morphs is ticked.

The top drop down box has the Body you will use, be sure to pick one that says Unique Player. If you don't, your body will look like everyone else's. I use CBBE Body [Unique Player]. Then select the preset you want to use and build the body.  When you go in game, your body will look different than the other NPCs.

HOWEVER, as this mod's title indicates, you do not need Unique Player to have a unique body.  You can simply use the built in BodyGen capability of LooksMenu.

FIRST - and MOST IMPORTANT, open Bodyslide, look in the bottom left corner next to the Batch Build button. Make sure that Build Morphs is ticked. Failure to do this will result in disappointment.

Next, open the LooksMenu folder, there is an ini in F4SE>Plugins>f4ee.ini.  Look through there and make sure that:

bEnableModelPreprocessor=1 ; Default[1]
bEnable=1 ; Enables loading of tri files and morphing meshes
bEnableBodyGen=1 ; Enables loading bodygen files to randomize actor sliders

These are all on by default, but check it anyway.

Now open Bodyslide and select the Body you want, such as CBBE Curvy, and select the Zeroed Sliders preset.  This is VERY IMPORTANT.  This sets all sliders set to zero.  BodyGen data ADDS to the sliders. So if you start off with a breast slider of 25 and your BodyGen data has a breast slider of 25, you would end up with breast slider of 50.  So you want to start at zero.

Next, Batch Build EVERY OUTFIT you have with the zeroed sliders. (Yes, every one.)

Next, run the game and open LooksMenu (console command: slm 14). Go to Body>Advanced. On the right side you should see a bunch of sliders. These are the BodyGen morph sliders. As long as the ini above is set right, you should be able to adjust those sliders and morph your body to whatever shape you like. And since you built all clothing with the morphs, everytime you change your body shape, your clothing/armor will change to match.

When done, accept changes and then save your preset.  Done. Your body is now unique from all other NPCs without the Unique Player mod.

---------------------------------------------------------------------------------------------------------------------------------------------------

But, you could spend all day adjusting sliders, perfecting your look. Maybe you already have a Bodyslide preset that you really like and want to use that.  Easy enough.

Download Body Convert.  On that mod page are the instructions on how to use it, I will not re-iterate those instructions here. Download and endorse the mod.  

What that mod does is convert Bodyslide to BodyMorphs in a .json format (the same BodyMorphs you were playing with above). Once you have converted your favorite Bodyslide preset to a json preset, you can save the file in ..data\F4SE\Plugins\F4EE\Presets (or the overwrite folder if using MO2). Save it with a new name from the other Bodyslide preset, such as MyPreset - BG, that way you can have both.

Load the game, open LooksMenu and load your BG preset.  Now you have the shape you like and it is unique from other NPCs. No Unique Player mod needed.

I have included a CBBE Curvy preset with BodyGen data. You can try that in game to see how it looks and works. You can also copy and paste the BodyMorphs data into a preset of your own.

---------------------------------------------------------------------------------------------------------------------------------------------------

But wait, there's more!

Now, you say, all the NPCS look the same, I'd like more variety.  Good idea!

Download and install Diverse Bodies by NoAbleEngles.  The instructions for use are on his mod page, I will not re-iterate them here. Download and endorse the mod.

What that mod does is take BodyMorph data and applies them randomly to NPCs (females only at this time). When used correctly, the NPCs in game should all look different. And since you can add more presets, up to 128 per folder, the diversity in the Commonwealth will become, dare I say...immersive.

So why use Unique Player and BodyGen at the same time?

Basically, you'd want to use this when a mod adds something to a body that you only want applied to your character.  For instance, Robo Leg Outfits replaces one leg with a robotic leg.  If you built that through Bodyslide as normal, every NPC would have a robotic limb.  Thankfully, the mod authors included a Unique Player body, so only your character will have the robotic limb.  When combined with BodyGen, your PC will have a robotic leg and a unique body. You can see on the Unique Player under Requirements, there are a lot of tattoo mods.  (Yes, the ESL version of the Unique Player works with all those mods listed. Nothing actually references Unique Player.esp.)

I realize this is more text then people want to read, but it's not terribly complicated once you wrap your mind around the concepts.  Hopefully, this clarifies and helps some people.

---------------------------------------------------------------------------------------------------------------------------------------------------

Credits: 
d_rail1602 for Unique Player and Unique Player Bods
nodtrial for Diverse Bodies by NoAbleEngles. 
zed140 for Body Convert
expired6978 for LooksMenu