Ventilate your surroundings. Mold and mildew can collect into nasty colonies when spores don't travel far---that's precisely what happens when the air in a home remains stagnant. Keeping air moving can prevent spores from settling and having the chance to grow. Ventilation also impacts the humidity and temperature levels of the home, which also affect fungi.
Control the temperature. Although fungi can propagate at all temperatures, most species do best at 75 degrees Fahrenheit or above. Keeping the temperature a bit on the cooler side thus creates an environment that is not as conducive to fungi growth and ensures that the fungi will have a harder time reproducing and growing.
Keep track of the moisture level. Just as fungi like warmth, they also like dampness. This is one of the main reasons fungi are most common in bathrooms, basements and around piping. To get rid of fungi, you have to keep things dry. Use a dehumidifier if you have to, and make sure that you clean up any spills that may occur.
Go over hard surfaces with a mild bleach water solution. Bleach kills and disinfects many types of fungi. This approach won't work on woods or materials, however, because the solution is water based---even though the solution has bleach in it, the water creates a moist environment that may promote fungi growth in the long run if the water cannot fully evaporate quickly enough. It works better on counter tops, in fridges or similar areas.
Get rid of organic material. Most types of fungi use organic materials such as newspaper and food peelings as food sources. This is why old books sometimes have a musty odor---tiny fungi are using the paper of the book to survive. Getting rid of these materials if you do not need them ensures that fungi will not have a good environment on which to colonize.
Dry it up and sweep it out. The majority of fungi cannot survive dry conditions, so if you have mold on things like canvas, get it as dry as you can. Then take the item outside if possible and sweep the material gently with a soft brush or broom.