You're looking for the debug command. If you want lots of output, you can just do "debug all" and that will show you just about everything the router's doing, on a busy router, this will easily overwhelm your console connection, so you'll probably want to narrow it down. Generally, to see all packets, you can do a "debug ip packet", you can add an access list number to this command, to see only those packets that match an access list. To specifically see packets on the serial interface, do a "debug serial packet".
Use the "?" in the middle of typing the command to see what other options you might have.
Hope this helps.