Here's a simple way without Active X that will work in older revs of Labview as well as Labview 6.1.
Have a string control on your front panel for the operator to enter a URL. Have a button (with mechanical action latch when released) wired to a case. Inside the True case, call System Exec.vi with the command line "c:\Program Files\Internet Explorer\iexplore.exe" (including the quotes) concatenated with a space and then the contents of your string control.
If you want to use a browser other than Internet Explorer (or if your iexplore is installed somewhere else), just change the command line.
See the attached Labview 6.1 example.