Multiple customers can access your application via Remote Desktop Connection on condition that the application is designed to support concurrent users, and runs on Windows server with properly configured Terminal Services. The amount of required modifications is minimal. The number of server client licenses matters.

Otherwise you will need to convert your desktop application to Internet-based application. That means a substantial amount of changes. A conversion process may take from 1 to several months for a small to medium database & application.

At least one place (not only) where you can find very decent source of information -- West Wind Web Connection in particular. There are also several articles on the site on that matter.
http://www.west-wind.com/