The StackOverflow FAQ (https://stackoverflow.com/faq) has this faq entry:
Are there any search options?
Indeed there are. Advanced Super Ninja Search Options no less. Visit the search page to see them … but you must first snatch this pebble from my hand, grasshopper.
But shouldn't there be a "Search Help" link just to the right or underneath the Search field that points to the https://stackoverflow.com/search page?
There is precedence for something like this. Notice that the main Google page (http://www.google.com) has an Advanced Search (http://www.google.com/advanced_search?hl=en) link immediately to the right of the search field. This would help out users that are new to the StackOverflow site.