You downvote by clicking the flag icon at the top right of any post. Flagging a post is a downvote.

You can tell if someone has downvoted you by going to the post in question and clicking on the triangle next to the number of votes. It will then list all voters on that post in order of their voting power. If any voters have a negative sign (-) rather than a plus sign (+) by their name, then they downvoted (flagged) you.