Before you can do anything, you gotta actually find where the templates are and where to put your custom creations. They're located under the art of rally livery folder, which can be found with the following filepath:
After you've located the livery file, you can choose a vehicle group in which to edit.
Then, choose a vehicle. Pretty simple stuff so far.
For my example, I'll be editing the Esky v1 .

First thing's first, open up GIMP. It'll look kinda confusing if you're not familiar with it, but It's not too complicated once you start using it.

After you've opened up the program, you can drag+drop the .PSD file into GIMP and it's ready to be messed with.

After you've done this, it should look something like:

From here, notice the two sections on the side, "Texture" and "UVs". The Texture layer is the part that will be visible on the car after you've finished making a design.
The UV layer is the drawing of all the different car parts, like a template. Be sure to make this layer invisible before finishing, otherwise your car will look like a grid.








Let's start by changing the color of the tires. Now, when changing the color of a part, you don't have to stay within the lines unless you're trying to isolate it from other sections of the same part. For example, to change the color of a set of tires, you don't have to meticulously color it in. You can simply use a select tool (as shown in the image to the right) and use a bucket fill. NOTE: When doing this, make sure you have selected the TEXTURE layer by left clicking it on the right side of the screen!






Here, I've used the bucket-fill to change the area around the rim to a bright red.















Now, if we want to see this appear in-game, we'll have to export it to a .PNG file. To do this, click on "file" in the top left of the screen. Then, navigate down to "Export as". This will bring up the exporting dialogue. (I've already exported it once before, so it gives me the option to export it to the same file again).

















Here, you can rename your creation (this will not effect the template) and change the file format to .PNG (as shown). NOTE: Whenever you want to save a livery, do not hit "save". Always export to avoid overwriting the template.






After you've done so, open up art of rally, go to any race where you can select a car, and your livery should show up at the end of the available liveries list. Since the tires were the only thing I changed, they're the only thing that will look different. You can experiment with different tools, colors, parts, etc.