This tutorial assumes that you are familiar with Unity and any graphics editing software. It makes use of Photoshop, but the same can be done with Gimp, Paint.NET, Pixelmator, etc.
First, take a screenshot of your game in Unity (in play mode) and load it into Photoshop. The game showcased in the following screenshots is Angry Bots, one of the official Unity demos.
Next, you can start tweaking the colors by using Adjustment Layers. Add as many layers as you need. You can also use the options in Image -> Adjustments if you prefer, but adjustment layers are better in every way (non-destructive, can be edited afterwards, easier to copy/paste etc).
Once you're happy with the result, open the neutral LUT located at /Colorful/Resources/LookupSource.png.
Copy all the adjustment layers you put on your game screenshot and paste them onto the LUT. If you did use Image -> Adjustments instead of layers, you'll have to reproduce the exact same step on the LUT.
Save the LUT as a new PNG file (it's good practice to keep the neutral one and not overwrite it in case you need it later). Import it into Unity, and set the texture options as follow :
Final step : add a Lookup Filter component to the camera (Component -> Colorful -> Lookup Filter) and drag your LUT into the Lookup Texture field.
And you're done. You've just used Photoshop to add color grading to your game ! It's very easy to do, very powerful, and only adds one draw call to your scene. In case you're wondering about hardware support, it only requires a Shader Model 2.0 compatible GPU.