Here is a post on Director responsibilities.
You can also consult the Articles of Association.
@nick.eth is better placed to provide more information here.
Approval voting is the same voting method used for steward elections, which you can see here with the last vote to elect Ecosystem WG stewards: Snapshot
To vote, delegates will be asked to select each candidate they approve of for the director role.
Delegates will be able to select as many or as few candidates to approve as they like.
At the conclusion of voting, the top-ranked candidate will be appointed as a director of the ENS Foundation.
Here is a link to Snapshot docs explaining approval voting.