In my experience, mold and mildew stains in bathrooms seem to be caused by two factors. One is the lack of adequate ventilation which causes moisture to build up which then condensates and creates an environment for mold and mildew to propagate. Having adequate ventilation allows moisture to be expelled and diminishes the opportunity for mold or mildew to grow.

The other factor is the paint. A lot of people don't pay attention to the paint that they are using, I mean, paint is paint, right? Well, not exactly. Semi-gloss and high gloss paints have anti mold/mildew properties. That glossy sheen creates a barrier that inhibits mold growth and thus this type of paint should always be used in moisture rich places like bathrooms and kitchens and maybe even laundry rooms.

Removal is fairly easy. You will need to roll up your sleeves, put on a pair of rubber gloves and get to it. With a mixture of bleach and water or better yet, a good stain remover from your local hardware store, you apply the affected areas and let it do its magic. After several minutes grab your brush and start brushing. Once the mold/mildew is removed to your satisfaction dry any excess moisture and let dry. Use a portable fan if possible to speed up the process.

Once the walls are dry, apply a couple of coats of stain blocking primer. Make sure you tape up any trim or fixture you don't want painted with masking tape. Once the primer has dried, you can proceed to applying two coats of semigloss in your desired color. Make sure you follow the paint manufacturers directions to insure a long mold free bathroom experience.

As I am installing a garbage disposer for a customer, she mentions that she will move some items from the kitchen counter top so I have more room to work. I say thank you. Two seconds later BAM! No, it's not Emeril Lagasse spicing it up a bit in the background on TV, it's my hammer. 

As my customer moves thing away for me to work, she inadvertently drops my hammer onto her tiled kitchen floor and hence adding a crack to one of her floor tiles. The damage was done.

Luckily, I knew what to do. The first thing I did, and you can too if you have the tools, was to chisel out the grout around the damaged tile. Do this carefully as you don't want to damage adjacent good tile. This is done so that when you go chisel out the broken tile you don't pull up non damaged tiles. This is the same concept you see in concrete sidewalks. Have you ever noticed the lines or grooves cut into the concrete creating a series of squares or rectangles as you walk? What this does is basically stops cracks from moving beyond those points and confining the damage to a relatively small area that can be later repaired.

Anyway, after you remove the grout around the damaged tile you can begin the process of chiseling out the affected tile. Remember to remove as much of the mortar under the tile as possible. Once the mortar is removed you will need to vacuum a lot of dust and debris left over from the demolition. Home Depot, Lowes or your local home center should have replacement tile if yours aren't from the 1970's. Otherwise you may have to use a similar design or find tile from a online supplier. You can also find ready made mortar and grout mix to use to set the tile and use the same mix to grout. Several color options are available. Use a grooved spatula to spread mortar mix onto the tile. Set the tile and use a level to make sure it's level all around. After grouting, use a specialty sponge, also found at your home center to clean up excess grout. Use a diagonal stroke as opposed to wiping along the grout lines as this may cause more grout removal than needs be. And there you have it...