If you've already created multiple iTunes libraries, when the pop-up window appears, click the "Choose Library" button.
Another window will appear, defaulting to your Music/My Music folder. If you stored your additional iTunes libraries somewhere other than that, navigate through your computer to the location of the new library.
When you've found the folder for your new library (either in Music/My Music or elsewhere), click the folder for the new library. When you've done that, click the "Choose" button. No need to select anything inside the folder.
With this done, iTunes will launch using the library you've chosen.