Head to the Events and Activities page.
Click on "Moderation" and you should see all of the activities.
These are broken down into "Pending", "Approved" and "Rejected".
Pending - activities that have been added but have yet to be approved for the central page.
Approved - activities that are live on the central page
Rejected - activities that have been rejected and so are not live on the central page
To approve pending activities, just click on the picture.
In the pop up, if you click on the top half of the picture, it opens up their public booking page, so you can see what that looks like. If you click on the buttons at the bottom, that lets you Edit the page setup (including booking rules, capacity etc) and Reject/Approve the activity.
If you click "Edit", you are taken to this page (make sure you click on "Booking Settings" when it opens):
Here you can check all of the rules and update any descriptions or pictures.