There are 2 common tools for this type of job. 1 is the Dremel Tool. It's mechanical, and if you're not careful, you'll damage your tiles! It spins at a high speed, and if it 'catches' anything, it will go off-center.
The other is a hand-held, non-mechanical, grout tool. It's a bit hard on your hand but safer. If your grout is dry and crumbly, it will be just fine since the grout will come up reaaaaal easy. (It's when the grout is hard and packed that this tool may 'wear you out'.) A roto-zip tool may be OK to use but you may have to rig some sort of 'jig' to keep the tool from damaging the tile.
In short, look into all 3 tools. Time-Life and Reader's Digest have good home repair/improvement books. Just check into seeing if they address repair/replacement of the grout AS WELL AS installation. Try the books at Home Depot, Lowes, and the like. The store's Tile Section may even have a 3-5 page handout to give you on how to do this job. Good luck!