Guidelines for ODBC and the internet

I need some specific guidelines to program an internet VB and database program. I do not want to use web pages. Here's what I want to do:
My program has a small database of our business' clients and their service contracts. We use it to know if a certain client has a service contract with us and has paid for it too. We want our other office in city B to open remotely the database (on a PC in city A) through the internet. We want our users in city A and B to use the same VB client I programmed.
My program is in Visual Basic and uses ODBC.
I have no internet programming experience, but I do have over 10 years of C++ and 2 years of VB experience.
What are all the steps I need to go through to achieve this.

Thank you all in advance
Paul