Most of the chucks are pressed together and to disassemble them, you need to press them apart. Just do a search with the chuck brand and "repair" or "disassembly" in the search bar and you will get millions of pages of somewhat useful info.
As for removing an arbor, wedges are the preferred method, especially if you want to salvage the arbor. However, sometimes there isn't a ledge for the wedges to push against, so other options are to drill a hole in the front of the chuck and use that to drive the arbor out (I hate this method), or you can just sacrifice the arbor and cut it off about 3/4" from the chuck, then drill and tap the remaining stub, then use a pipe coupler, some washers and a bolt to extract the remaining stub.