Start with simple steps:
1) Bird, reptile, and rodent cages should be cleaned frequently, and without fail.
2) If you have someone in your home who suffers breathing sensitivities, it is best to keep pets out of that individual's bedroom, and certainly off of the bed.
3) Wash your pets often to prevent excessive dander. Think about how you feel if you haven't bathed for a while. Just because pets attempt to lick themselves clean, does not mean that they should not be bathed when living indoors.
4) Frequent dusting and vacuuming is essential to controlling airborne allergens. In order to trap the allergens and prevent them from being blown back into the air during vacuuming, the vacuum should be equipped with HEPA (High Efficiency Particulate Air) filtration, or at minimum, the best quality bags available should be used. When dusting, use damp or treated cloths and mops to trap the dust and prevent it from becoming airborne again.
5) Dogs that urinate or defecate indoors will typically do so because of owner negligence. Either the owner did not take the time to properly train the dog, or the dog is made to wait too long before going outdoors. Remember that dogs would rather go outdoors than indoors if given the choice. If you have a dog urination or defecation problem, it is time to commit to a serious training program, or be more sensitive to your dogs need to go outside. Fortunately, dog urine is not as pungent as cat urine and therefore a little easier to eliminate, however, their urine and fecal matter can contaminate the air we breathe just the same.
6) Cat urination can cause a tremendous amount of damage to a home. Remediation costs can quickly range from hundreds of dollars to many thousands of dollars. Some cats will urinate around a home to mark territory. This often occurs when a cat is moved into a new home or when another cat comes to visit. Other cats will urinate around a home simply out of desperation due to owner negligence of the cat box. To prevent this, there should be one cat box for each cat present and the boxes should be cleaned on a daily basis. Cats can be quite finicky and will readily go elsewhere if their boxes are dirty, or if they have to share a box with a different cat. Cats will usually be faithful to their boxes if they are kept clean.