You can use a sharp grout removal tool but you do run the risk of leaving marks on the tiles or worse still, you could chip the tiles. You will need to be careful.Agreed with the previous responses, use a good grout cleaner, or strong cleaning agent. Assuming the tiles are not natural stone.
Use a good scrubbing brush, the harder, probably the better. Spray on the cleaning agent, agitate with the brush, Leave for a few minutes, scrub the joints and wash down with a clean white cloth, Not coloured as the dye may run.
This may help. Please remember to read the instructions on the cleaning agents for recommended usage. Good luck.