SilverStripe works on a remote server, like a web host such as DreamHost (http://www.dreamhost.com). Multiple administrators can login to the CMS at the same time to edit content, however there is no functionality to 'lock' pages or anything of the like at the moment.
There is, however, staging supported - for example, you can create draft copies of pages for your site in the CMS, then when you have someone approve the content you can then publish the 'draft' version which shows publically to the world.
In terms of editing files, like Will said, a versioning system is ideal for multiple people editing the site files - html, css, js and php files for example. Here at the office we use SVN which comes in handy for more than 2 people working on a single site at any one time, and for multiple sites sharing code.
One possible way of creating a new site using SilverStripe would be to develop it on your local pc. Then, when you feel it's ready for the world to see, you'd then upload it to a web host.
Hope this helps,