Inhalation. Depending on the size of dust particles, they can enter your mouth and nose and be caught in nose, mouth, throat or upper respiratory tract, or if they are small enough, they can travel further, to lungs. Possible health effect include pneumoconiosis, fibrosis, silicosis, lung cancer, extrinsic allergic alveolitis.
Skin contact. While contacting your skin, some dusts may cause health problems like dermatitis (e.g. wood dust or fiberglass).
Eye contact. In case dust contacts your eyes, it can be a source of irritation or mechanical damage of tissue.
Ingestion. When dust particles are blocked by mucus in your mouth or throat, it can happen that they are swallowed, causing e.g. gastrointestinal tract irritation. Poor hygienic practice (not washing hands) may result in allowing dust particles to enter the organism through hand-to-mouth contact.