Building an area for users to add content for Craft site
Welcome to Craft!

For starters, I would definitely recommend checking out the Pixel and Tonic Guest Entries plugin, brought to you by the guys who built the CMS. As the title suggests, it allows users to create entries from a custom form on the website front-end.

So, from your example, you can have an 'Events' channel and allows users to create entries (events) using the form.

These entries can then be moderated like any normal entry.