How are US Senators and US Representatives chosen?

Under most circumstances Senators are chosen by popular vote in a State wide election in the State they represent. Occasionally when an incumbent Senator dies or otherwise leaves office the Governor of their State will choose a temporary replacement, depending on the laws in that state the replacement will finish the term of the exiting Senator or will serve until a special election is held.

US Representatives are chosen by popular vote in the congressional district they represent. The manner in which they are replaced varies from state to state.