Texture becomes black when tryng to bake vertex color to texture! when I UV smart project my model, then open a new file (thats black) where I want my vertex color to bake to. The texture only becomes black. It doesnt make any sense.
Please look at attached file:
https://gyazo.com/045b606b616df5907c79aaf2cf10d7e0

I have multiple guns that I would like to bake a texture from. So please post an explanation when you fix the gun. Thanks! 

Here is the gun (Glock 18):


EDIT:
Hey, I used the answer that Craig wrote. Basically, I got the colors etc. But the texture was very "round" compared to Craigs. 
I do not know why. 

What I did:
(Firstly changed from Cycles to Blender Render)


Make the whole model "one", so I can edit the whole thing at once.(CTRL + J)
Smart UV Project the whole thing.
Add blank, black image.
Go to bake, choose Textures. And Bake the whole thing.


WHAT I GOT: (Please see attached link)
https://gyazo.com/be11838d12f9b26fc78943d09faec235


  When I used the texture on a Model in ROBLOX STUDIO the model just went black.
  (See link)
  https://gyazo.com/9f3838c2061a552da4361bbf32b881f1


Why??
What have I done wrong?
Why does it look so different from yours? (I know I did something wrong!)
Please tell me. It would mean the world to me! Seriously, I got to get the game out in February! Thanks!
You have no vertex colors, your file has blender render materials but is set to Cycles right now. Turn it back to Blender render. In your scene, you have no light source, so every bake will be black.

edit: My steps were incorrect the first time, so here is a corrected flow:
1. Your file as it is with Cycles as renderer but has no Node materials.

2. I switch to Blender Render and find your UV are wrong, so I Smart UV Unwrap

3.I also then remember in Blender Render that I can bake using Textures to get the straight diffuse color without a lamp

And then the result comes out pretty clean