Well, since you are specifically asking about the process, this appears to be a hand painted job so there probably is no exact match. Also, since the font is distorted it makes it very difficult to use any computer program to try to identify the font. Therefore, there is only one method left, you can try a few fonts that you might know from experience, otherwise you just have to start searching. Focus on some unique element such as the serif on the R, the style of the C or the single left side serif on the A, then go through your installed fonts using any software that will allow you to type out ARCHER and view it in different fonts. After that you could use a web based service such as What the Font or What Font Is to search fonts that you don't have. Finally, you go on Signs101 and ask for help!