How to search for selected text in Vim?

You can yank the hightlighted text first. Then

• /

• Ctrlr

• "

Which will paste what you have yanked after the /.

The following sequence will do what you want, given an already selected block of text:

• y (yank the selected text, into the " register by default)
• / (enter search mode)
• (\ V) (optional, enter "very no magic" mode*)
• Ctrl+r " (insert text from " register)
• Enter (Engage!)

(*) "very no magic" mode interprets the following text as plain text instead of as a regex. note however that \ and / are still special and will have to be handled in other ways. If the text does not have any characters considered special, you can skip this step.

Source: Vim Tips Wiki

I never felt the need for such a feature but, considering you can find a need for any feature on Vim, I think this from the Vim Wiki should help:

vnoremap // y/\V<C-R>=escape(@",'/\')<CR><CR>

I didn't test it but, looking at the code, it seems to be exactly what you're searching for.