How do I designate others to become moderators at our group site?

I ume you are the owner of that Group (because you must be to appoint moderators). If so, then log in to your Group's web site. Then click on Members on the left-hand side of the page. Then go through the list until you find the member that you want to promote to moderator. Just under this member's login name will be an Edit Membership link (pencil icon); click on it. Then click the Change To Moderator link down in the Membership Privileges section. Then, in the Moderator Privileges section towards the bottom of the screen, check each box that represents a privilege you want to give that moderator (it's common to give all the privileges in the left-hand column, but be very picky about which privileges in the right-hand column you give him/her). Don't forget to click the Make Moderator on (towards the lower-right-hand corner) when you're done.