Connection String while Publishing

I have an application that I have been developing over the last couple months in Visual Basic, using Visual Studios 2010 Ultimate. I have completed and linked all forms together and now it is time for me to begin linking objects, such as my DataGridView to my SQL database. No problems with connecting to my SQL server, or using SQL commands to SELECT, UPDATE, etc. But trying to be proactive and look at the future, I can see the issue of when I publish and implement the program on someone elses computer, they would be able to connect to my SQL server. How do I set up the project so that when a client installs my application, they can use there SQL server? Do I need to have an installer that would install not only my application but SQL server 2008 and replicate the original database that I had worked with when creating my application, I.E. dataset, SqlTableAdapter, etc.?

Still a bit new to programming and SQL(<3 months), so if it doesnt make sense, please let me know and I will attempt to reword it or provider additional information.