If the existing grout is still solid and can't easily be scraped out, then you can overcoat it with Davco Rejuvenation grout. Existing grout must be at least 1mm below the tile's surface, allowing sufficient depth for the rejuvenation grout to bond to the grout joints. The tile and grout surface must be thoroughly cleaned with either a mild soap and water mixture or a sugar soap mixture. If required, a bristle brush can be used to clean the existing grout joints. Following the cleaning, rinse the surface with clean water.
If the grout has deteriorated, become powdery or is falling out, you'll need to remove it. A multi-tool with a diamond blade is the most effective way to chase the loose grout along the joints until you hit solid material. You'll then be able to re-fill the joints with an appropriately coloured tile grout. I recommend Dunlop 800g Ready-To-Go Coloured Grout as it has an easy to use application bottle and comes in a variety of colours. - MitchellMc
I remove the damaged and cracked grout and fill the joints with new grout. As only a few joints are affected, I was looking to use the Dunlop Ready-To-Go Grout that comes in a bottle. - Navz