This is a port of one of the many visual-star plugins for Vim to work with evil-mode.
Install evil-visualstar from MELPA.
Add (global-evil-visualstar-mode) to your configuration.
Make a visual selection with v or V, and then hit * to search that selection forward, or # to search that selection backward.
If the evil-visualstar/persistent option is not nil, visual-state will
remain in effect, allowing for repeated * or #.
Note that you than have to exit visualstar-mode before hitting a direction key to avoid extending the selection.