Option 1, purchase a separate copy or seat license of FileMaker Pro for each user. Since each user has a different install code you can host the file with FileMaker ( up to 9 simultaneous users ) or FileMaker Server (Many more users and much enhanced tools for managing a shared database.) and each user can connect using the Open Remote... option. I don't think VPN is necessary for this type of connection.
Option 2, Use Instant Web Publishing to host the file to the internet or intranet. Users (up to 5 at once when FileMaker Pro is used to publish to the web, many more can connect if you use FileMaker Server Advanced to publish it.) can connect to the database via their web browsers. This option is more technically challenging to set up and places limits on how you design your layouts and scripts in order for them to work correctly within the limits of the web browsers, but saves you the cost of purchasing a copy or seat license of Filemaker Pro for every user. VPN is not needed for this option either.