I actually set mine up for my son & his classmates.

Simply put, create a vhost that has it something like this:

ServerName your.domain.com
ServerAlias *.your.domain.com # <-- This will be the multi-site bit

In DNS, make sure you have *.your.domain.com pointing to your server. Yes, DNS allows for wildcard domains.

Next: follow this guide:

Guide to Creating a Network

Finally:

as admin, install ONLY plugins you trust. Same goes for templates.

Sub-sites on multi-site installs cannot install plugins or themes, but can use all the ones you have installed. Inversely, they are not required to use a plugin or theme you have installed.

If you really want a well-rounded view of what is happening, I recommend Mika Epstein’s e-book on WordPress multi-sites:
http://store.halfelf.org/ebooks/wordpress-multisite-101/

She is best when it comes to multisites

Thanks for the replies!