You will have to code the connection manually to connect to a remote MySQL database using Visual C# 2008 Express Edition.
VS 2008 Express (and VS 2005 Express too) doesn't allow you to use MySQL .Net Provider through the Data Source Dialog. The non-Express edition allow you to do the same.
To use MySQL in VS Express, you will have to include a reference to the MySQL DLLs. If you have installed the MySQL .Net Provider, the DLLs will be in C:\Program Files\MySQL\MySQL Connector Net x.x.x). Or copy the DLLs to the Bin folder of your project. After including the DLLs, you can make a ConnectionString to connect to the remote MySQL
Database.
The MySQL .Net Provider can be found http://dev.mysql.com/downloads/connector/net/5.2.html
A similar question was asked in thread http://stackoverflow.com/questions/396593/mysql-net-provider-5-2-does-not-show-up-in-data-source-dialog-of-vs-2008-express