Using a Droid Customization Kit, you can change the color(s) of your droid. To accomplish this, you will need to pick up a Droid Customization Kit from a local engineer. Place the tool on your toolbar and call out your droid. Target the droid and use the tool, from your toolbar. This will bring up a window with a couple of options, depending on the droid.
Some droids will have the option to customize the Frame and the Trim. Others will only have an option for Frame. Once you select one of these, a color palette will be displayed. Selecting a color will change the color of the droid. Selecting OK will make this change 'permanent'--at least for the next 2000 calls.
The following droids can not currently be customized through the use of a Droid Customization Kit - Protocol Droid and the Mk3 Mining Droid. The Protocol Droid does have an option to customize its color, during the crafting process.