I've had two members wishing to post announcements. When sent to me for approval, I click 'yes' and am unable to see their post. Thoughts???

Welcome Stacey.

Here is the procedure for approving Announcements submitted by members:

1) Click your Post Announcement link.
2) Click the Edit button next to the Announcement that was submitted by the member.
3) Place a checkmark in the active column.

Placing a checkmark in that active column is what approves the Announcement to go live on your site.

Can't...their posts aren't showing up on the post page.

If that's the case, then the Classmate deleted their own Announcement. This usually happens when a Classmate is just testing the system to see how it works. If they post and delete and Announcement before you've ever seen it, then, you never see it.