Okay, this is the last of the constitutional policies regarding the House of Representatives:
When vacancies happen in the Representation from any state, the executive authority thereof shall issue writs of election to fill such vacancies.
The House of Representatives shall choose their speaker and other officers; and shall have the sole power of impeachment.

Okay, now we’re getting into the specifics of how representatives are chosen for each state. Remember the main point of the bicameral legislature is a group of two senators for each state and then a certain number of representatives elected based on population. Here’s how they figure it out:
The actual Enumeration shall be made within [...]

Okay, this parts a little complex. As I’ve said, this is a splice in the original document stemming from the enactment of the Fourteenth amendment in 1964:
Representatives and direct taxes shall be apportioned among the several states which may be included within this union, according to their respective numbers, which shall be determined by adding [...]