A good start is to restrict which rooms your pet is allowed in to. Avoid letting pets in to living rooms and bedrooms which have a lot of fabrics and carpets which will easily collect pet dander.
You can never remove all traces of dust mites. Use a damp cloth to dust hard surfaces and floors regularly to reduce build up of dust and dander.
You can never remove all pet hair and dander. Even the most efficient vacuum cleaner can’t remove all dander. It remains for months or sometimes years and can still cause symptoms despite regular cleaning, even after the pet has been removed.