Setup a website with the home folder set to the location of your files.
The website should use SSL unless security is zero concern
Enable WebDAV for the site
Enable folder listings
Add a realm (password protection) for the site, include users/groups that need access
Users can access the site with a web browser to download files.
To upload they would need to make a webdav connection (doesn't always work great, depends on several factors)
You may want to consider Rumpus.. Its a web-based file manager.
Simple setup. Very reliable. Works with any web browser.
Look specifically at the Web File Manager features