How to PERSONALIZE THE SEARCH FORM

As all WP users, I have a search form limited to an only input-text field, that searches in all posts.
How to personalize the “search form” to let the user to select (with radioboxes and checkboxes) where realize them research (which wp-categories and wp-custom-fields).

Or does exist a plugin to do that ? (Not a plugin like “search unleashed”…).

Here’s my “search form”:

<form method="get" id="searchform" action="<?php bloginfo('home'); ?>/">
<input type="text" value="<?php echo wp_specialchars($s, 1); ?>" name="s" id="s" />
<input type="submit" id="searchsubmit" value="FIND" />
</form>

Thanks to anyone can help me!