Some places use a service like DropBox where you can allow specific users access to a folder or documents.

Some places have their own home-grown applications that allow sharing of files through a web interface, although this is usually done as an upload, download, modify, send back sort of interface.

Some places use something like SharePoint, where you can invite people and all collaborate on the document in the SharePoint site (I believe it requires IE to use the online editing though).

Most places I've worked at typically would create a network share and give specific users VPN access to modify and update the files.

It all really depends on who the target users are and what the end goal is.