Prerequisites to setting up GBA <-> GameCube Emulation
DSP-LLE Dumps from a GameCube or Wii may be required for some titles. While DSP-HLE will work, DSP-LLE will experience higher compatibility and more stability. This may not matter in most titles, but in Final Fantasy Crystal Chronicles and Animal Crossing, many features will not work without DSP-LLE.
Game Boy Advance BIOS is required for most titles. Any game that connects to a GBA without a game running requires a GBA BIOS in place. The easiest way to dump a GBA BIOS is through a GBA Flashcart.
When those two things are in place, you must configure both VBA-M and Dolphin to connect to each other. In each VBA-M Instance, you must go to the file menu and select "Connect to..." and select GameCube (Dolphin.) In Dolphin, you select "GBA" under each GameCube Port you're using as a GBA under controller configuration. Startup Dolphin, and get to the point where the game wants a GBA connected, and then bootup the GBA BIOS (or game; if it wants to connect to a game.) Connectivity should ensue, and if all goes well, the emulators will sync up and communicate to one another.