It's pretty simple, really. First, I looked up what the JPEG format is like. It turns out it is quite simple and always starts with a specific unique header. Then, I simply popped the whole ROM into a hex editor and searched for that header. The headers tell you what size the image is, so I used them to copy the image's data, pasted it into a new empty file, and saved it with a .jpg extension.
I'm still working on Clock Town, and I have all of the interior areas done except for those in the east area. I'm working on the Milk Bar (probably the most difficult) and still have the Stock Pot Inn, Mayor's place, and Astral Observatory to do. Oh, and the Clock Tower face from the Final Day. I'm going to try to finish this map soon, or at least before July ends. It would be quite sad if a single map took me a whole year to complete.