Remove the crumbling grout from each molding grout line, using a grout saw to dig it out. Break up the grout by pressing down on the saw with both hands and pushing it forward and back, until it starts crumbling. Get out as much grout as you can from each area where it's moldy.
Vacuum out the debris from the grout lines with a vacuum hose.
Mix grout mix and water in a bucket in the amounts called for on the grout packaging for your size of project. Use your drill and mixing bar to blend the grout well.
Let the mixed grout sit in the bucket for 10 minutes. Restir with the drill and mixing bar.
Use your grout float to scoop up a trowel-full of grout and press it directly to the first dug-out line. Press the grout into the line by scraping the edge of the float in a diagonal direction to the line. Fill all the lines that you dug out, scraping off as much excess grout from the surface as possible.
Let the grout to sit in the lines for 10 to 15 minutes. Wipe up the residual grout with a damp sponge. Let it set 48 hours.