After activating visual mode and selecting some text, if I hit / to search forward and then press <C-R>*, I get the selected text inserted into the command line.
Another way (at least in Linux) is to press <S-Insert>, which will insert the contents of the current selection in X11 (e.g. select something in firefox and you can <S-Insert> in any other application to copy that selection; again, at least in Linux).
Keep in mind that with your specific example, after you insert some text after the / command, your visual selection will expand to include the next occurrence of whatever it is searching.
Edit: I was assuming GVim, which copies the visual selection to the X11 selection buffer (see :help x11-selection for more info).
If you are using Vim inside a console, then I think (but could be wrong) that your best option is to select the text you want with the mouse while pressing Shift down, and then use <S-Insert> to copy that text into the command line. This works in Linux and probably in OSX too; I don't know about Windows, sorry.