If you want to run FSO from Visual Studio you need to tell Visual Studio where your game data directory is.
I) You need to add an user environment variable:
1) Right click on "Computer" or "My Computer" and select properties.
1a) If you are one Vista or 7 you will have to then click on "Advanced System settings" in the left hand column. Depending on your UAC settings you may or may not be prompted to elevate your permissions.
2) You should be looking at the "System Properties" dialog.
3) Select the "Advanced" tab if not already selected.
4) Click on "Environment Variables" at the bottom of the window.
5) Another window will pop up. Check in the "User variables for <user name>" section to see if you have a variable called FS2PATH.
5a) If you already have one called FS2PATH, select it and click edit.
5b) If you don't have one called FS2PATH, click new (remember under "User variables" not "System Variables").
6) Set/verify that the variable name is FS2PATH and the the value is the fully qualified path to the data directory that you want to use (that is it starts with a drive letter).
7) Click Ok for every dialog.
8) Restart your computer (seriously, these variables are only set during boot).
II) Open the Freespace solution file.
1) Right-click on the Freespace2 project and select properties.
2) Change the "configuration" to "All Configurations".
3) In the tree on the left select Configuration Properties > Debugging.
4) Click on Command in the right hand window, and click the down arrow on the far right.
5) Click edit in the drop down menu.
6) In the dialog that comes up enter exactly the following:
$(FS2PATH)\$(TargetFileName)
7) Click okay. And click okay again for the Property Pages.
You can now just select the build variant that you want from the drop down at the top center and click the green arrow and Visual Studio will automatically build the binary, then copy the new binary to the game data directory, and then start the binary with the debugger attached.
There are several other variations of this procedure that have other advantages but this is probably the simplest and most pain free becuase you can then forget that you did it after you get it setup (like I did

).