Jolene - the best way I know of is to remove the old grout with a grout saw (available at Home Depot). Buy the kind that takes replacement blades, and buy about 4 additional blades. You may find the job easier if you apply water work the joints wet.
Remove as much grout as possible, but most importantly, you want the square edges at the face of the tile clean and sharp - this will ensure a clean reapplication.
Clean the surface and exposed joints with diluted white vinigear, wash down with water and reapply grout when the tiles dry.