It's not quite that simple - your app can't just work with "any database", you have to decide which database system you are going to use (there are SQL Server, MySql, SqlCE, SqlLite, Oracle, and many, many others).
Then you have to install any necessary software on an appropriate machine (SQL Server and MySql both want a machine to run them in the real world - for development you can install them on your own machine).
Then it still isn't simple - but this should help:
VB.NET Tutorial: SQL Database Basics[
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