Once you have removed the old grout, you are now ready to replace it with new grout. Start by taking a soft sponge, dampening it with water, and then wiping it over the surface of the tiles and the lines between them.
Next, take your grout mixture – the mixture you use may differ depending on the tiles you have, so if in doubt ask for advice in the store – and tip it onto the affected tiles. Using a rubber flow, spread the grout all over the tiles so that it fills the gaps that you have just scraped out. Use the float at a 45 degree angle, and try to move from one corner of the tile to the other in a diagonal motion for the best results.