Dig out all damaged or loose grout from each grout line that needs to be repaired, using your grout saw. Use the saw by scraping it forward and back over the grout surface. Don't remove the parts of the grout that are solid and undamaged.
Clean the extracted lines of dust or residual grout, using a stiff paintbrush to brush it out.
Pour about an inch of water into a bucket. Add enough grout to cover it. Stir with a putty knife. Add additional grout and water, alternately, adjusting the ratio until you have the consistency of thick mud. Make enough to fill the open grout lines.
Let the grout sit undisturbed in the bucket for 10 minutes. Stir it again.
Use your grout float to scoop the grout from the bucket and press it into the open lines, while squeezing it off the surface with the edge of the float.
Let the grout sit in the lines for 10 minutes. Use a damp sponge to wipe up the residual grout. Let it set 48 hours.