You'll need some hardware-specific docs to help as well as a touch of ASM knowledge and an emulator with debugging functions (FCEUXD springs to mind), but here are the quick-kill steps to success.

1. Figure out where the tilemap is located in VRAM.

2. Set a write breakpoint to the first byte of that memory location.

3. Run the game till execution breaks. The instruction the game will break on should be either LD-something or STR-something; this is a LoaD (or SToRe) instruction and will save a byte stored in a register to memory (in this case, it should be the VRAM address). Look above it for another LD instruction: with a little intuition, you should be able to figure out which instruction loads the byte from the ROM that is written to VRAM.

4. Set an execution breakpoint to the load instruction. Next time the game breaks, you will have in your hands the address of the second byte of the game's tilemap. With a bit of conversion, you will know where to look for the tilemap in the ROM.

The tilemap data should consist of two parts: the tile data and the palette data (though on B/W games like those for the original Game Boy, there will only be tile data). How they are mixed together (if at all) will depend entirely on the platform and the title, but you should be able to figure it out easily enough. Once you can identify the palette information, you can proceed in one of two ways.

1. The Easy Way: Change the palette of the tiles to the existing palette you wish to use. The upside of this is, of course, that as long as you can somehow view the palettes used by the game, you will be able to change the color scheme of the tiles to anything you wish to use. The downside is that if the colors you wish to use are not included in any of the game's palettes, you're out of luck unless you do things...

2. The Hard Way: Change the actual palette data. This will require a bit more ASM skulduggery, but if you can find where the actual palette colors are stored in VRAM, you can work back from that using the above method for locating the tilemap to figure out where the palette data is stored in the ROM. After that...you can change any of the game's colors. Make all the Goombas bright green, turn Buzzy Beetles fuchsia, give Lakitu his very own Kinto'un (i.e. change his cloud to gold), move the Mushroom Kingdom to Gallifrey or Vulcan with a vivid orange sky...the possibilities are only as limited as your imagination. Then we have the downside: unintentional color changes. There's only so much space for palettes in memory, and some objects may use the same colors as other objects: if your plans for palette mastery begin and end with the game's title screen, you may inadvertently wind up changing much more than you bargained for.

I hope this helps. These techniques should serve you well with any game on almost any platform.