Even if there is no immediate pain or sensitivity at a broken tooth, it should still be assessed by a dentist as soon as possible. Leaving it un-repaired may lead to the tooth becoming sensitive or painful. Further, if not treated and repaired, a broken tooth may break further and may become irreparable.
Whilst you wait for your dental appointment to get the broken tooth assessed and repaired, clean out any debris in the area with warm salty water. If the break was caused by trauma, a cold pack on the outside of the cheek can reduce swelling and discomfort. If there is a piece of the tooth that has broken off, bring it in when you come for your appointment as it may be possible to bond the broken pieces back to the tooth. Keep the broken piece of tooth moist until you come in if possible.