There are various different techniques. A lot of rough features like the base coat can be applied using spray painting or brushing. Just have the models go through a paint area and get covered in paint. This can be done before the parts are assembled so the parts are different colors, but you can also get some different colors on the same part although it will be quite rough.
For better details the most common way is to use stickers. There are machines which can apply stickers to an object in roughly the right place. It is also possible to stamp the paint on the model. This is done with special stamps custom made for the model which fits the contours.
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