For pet allergies: Use an air purifier with a HEPA filter, vacuum frequently (vacuum should also utilize a HEPA filter), bathe pets at least once weekly, do not allow pets in your bedroom, brush your pet regularly outdoors and keep pets off of clean clothes.
For dust mite allergies: Use an air purifier with a HEPA filter, vacuum frequently (vacuum should also utilize a HEPA filter), use allergen-proof mattress, pillow covers and bedding, and keep decorative pillows and stuffed animals off the bed and out of the bedroom.