What is the easiest way to edit an Access database online?
Solution 1:
The simplest solution, although not necessarily the cheapest, is to allow your remote users access via Terminal Server/RDP. Now if you only have one user at a time using the app then you could easily dedicate a PC to this task and open a port on your firewall and route the traffic to that PC.
Also note that you should consider splitting your database into a front end and back end and allow multiple users to work with data at the same time on your local network. See See the Splitting your app into a front end and back end Tips page.
Solution 2:
Consider a switch from using Access to using MS SQL. Access (2007 at least) has Wizards to help you convert pretty easily.
SQL will give you the availability and multi-user capabilities you seem to require in your DB.