I have an EPROM programmer here. You burn the game to them (depends on the game size and EPROM size of course).
What I did is simple:
-Get a donor cartridge with SRAM and battery backup (cheap sports games).
-Desolder it's MaskROM (the actual game).
-Solder in the EPROM(s) and wire it correctly.
-Remove the original label with a hair dryer by peeling it off after warming up.
-Print the new label on glossy, self-adhesive photo paper.
For more informations about cartmodding visit this page
or this one (recommended for beginners)
Disregard the EPROM sales on the 2nd page. It's outdated.