Team Colors

Base Layer
Make sure you have white-light gray color on the parts where you will want team colors to be applied on top (dark base color will mess up the team color):

Mask
Then you will need a mask (diffuse texture). Example:

- Black - will leave original texture / no change here
- Red - marks where the game will put primary team color
- Green - secondary team color
Material
Set this mask as Diffuse2Map and check use_double_colormap_with_mask_texture:

XML
Then in XML in the item's description make sure you have:
Color Variations
You can give half values to the color mask textures, something like 0.5. Then it will use both the base texture and the faction's team color in a blended way:

With weapons
Sh1ny4: Since 1.3 some lances parts (the banner ones) have team color enabled, no idea of if it can be used on other weapons but at least we have some form of progress
Horse Armor Problem
Team colors on horse armors/caparisons are not supported by the game. Bug report here.