You will receive all messages to be moderated via e-mail. If you do NOT react, after 7 days, the message will be dropped and the sender will be informed that he has to send it again. So, if you forget one message, that's no problem.
To moderate a message through, i.e. to let it pass to the list, simply reply to the moderation e-mail, which will result into a recipient of firstname.lastname@example.org
You do NOT need to reject a message. If a message is spam, simply ignore it.
If more than one moderator approves the message, this is no problem either, as it will only be sent to the list once.
Sometimes, people do not recognize that they are sending to a mailing list, and than the e-mail contains private information like phone numbers. In such a case, feel free to ask the sender first if he wanted to send it to a public viewable mailing list.
If you moderate a message through, it would also be good if you sent a short notice to the list, telling that the message has been moderated. This way, people know they must copy the original sender in all replies.
Oh, and of course, you don't need to look into all messages. The more, the better, but due to the amount of spam it's totally normal that we miss some messages to be moderated, so don't worry about that.
There's also a mailing list for moderators. Feel free to subscribe via an e-mail to email@example.com to discuss with moderator colleagues.