It varies machine to machine; at the simplest end is the Neo Geo — its 68000 and Z80 have completely independent buses. You write one program for the 68000 and one for the Z80 and a single pipe of communication joins the two: post a byte to the Z80 and it'll trigger an NMI; the Z80 can read the command byte from a certain port and write a response to another, the 68000 can poll for the response. Neo Geo also supplied a sample set of Z80 code so you could just treat it as an advanced sound generator and not worry about the implementation if you prefer.
The Mega Drive has a more complicated system of shared buses; the Z80 has some memory on a private bus but the cartridge bus is a shared resource and I think the Z80 can also share some RAM. In that system the VDP can also act as a bus master so in net it's the Z80 getting access to the shared resources only when nobody else is attempting an access, the 68000 having priority only when it doesn't chose to start a VDP transfer, and the VDP having top priority for those periods when the 68000 has command it to do something.
If you ever hear scratchy sampled audio in a Mega Drive game then it's likely to be the Z80 trying to stream from the cartridge but frequently losing out on access slots.
The Saturn is like a more advanced Mega Drive except that the main CPUs have caches that can also be configured as small local memory pools. So if you're careful you can mostly keep them off the shared bus, gaining a significant performance benefit — Virtua Fighter 2 manages to keep most of the data for each player local to a single CPU for most of a frame, the laziest PlayStation ports do nothing in particular and either end up only using a single CPU or effectively doing so as a result of collection.
The Jaguar is supposed to work similarly to the Saturn but, quelle surprise, Atari rushed it to market so there's a significant bug affecting the RISC CPU's accesses to RAM when performing certain types of jump. That's how it often ends up being treated as a machine with a 68000 central processor when really the 68000 was intended just to be an intelligent scheduler.
So: across these systems one generally writes a different program for each processor, and either nominates one as a coordinator or uses a series of ad hoc means of point-to-point communication.
If it sounds hard to get right, that's because it is — programmers much prefer systems like the original PlayStation with a single CPU that just goes quickly.