Don't wait until mould is growing in your shower walls. If moisture has broken the seal between the grout and tiles in your shower and caused it to crack, the problem will only worsen over time. When you notice this problem developing, the grout should be removed and replaced immediately. Removing grout without removing the surrounding tiles isn't complicated, but it takes some work and patience. Plan on being without use of the shower for a few days.
Using the grout saw, extract all the lines of grout that are cracked. To do this, scrape the saw back and forth over the grout until it breaks down under the surface, then gradually dig it out. Make sure not to scratch the surrounding tile.
Use the vacuum hose to remove dust and debris.
Use the putty knife to mix the grout in a bucket with water according to package directions. Let it "slake" in the bucket for 10 minutes to make sure all the components meld.
Scoop up the grout with the grout float and press it to the tile with long edge tight against the tile face, scraping the excess grout off the tile. Work in sections you can comfortably reach from one position (generally, 4 to 6 square feet).
Let the grout sit in the lines for a minute, then wipe down the tile faces with a damp sponge to remove any residual grout.
Let the new grout set for at least two days. Then use a small brush to apply grout sealant over all the grout lines, both old and new.
Wear a dust mask when mixing the grout to avoid breathing in any particles.