Ah.
Where it says “Gmail” on the top left corner (under Google), click the drop-down menu and select “Contacts”. Scroll down to the people you’d like to remove, click the box to the left of their names, then look at the horizontal menu above this list. There will be a “More” dropdown menu. Click on this, then select “Delete contact”. This will remove the person/people from your contacts list.
Caveat: removing people from your contacts list does not ensure that you will never see their name or email address again. When you type a name or address into the “To” box while composing, these people may show up there. I think this is because gmail searches for addresses throughout your archived mail, not your contacts list. I think (though haven’t tested this) that you can only totally expunge a person’s address by deleting all mail to or from that person (that would include mail that was sent from other people, in which you were both recipients).
There should also be an option to tell gmail not to autocomplete addresses, which would have the same effect… but probably also be too great an inconvenience to make a good solution.