Hi!
How can I add text to explain how the search works, immediately under the search function (not after all the listings)?
You can customize almost anything (and our Themer’s Guide explains the basics for safely overriding and modifying our templates, so that’s well worth reading).
In this case for example you might override and add text to the modify/bar.php template – perhaps though it would work for you to add some text in the add HTML before event content field (found in Events > Settings > Display)?
Also, is there a way to format the search boxes so they look more like typical ones
You can certainly apply custom CSS styles … but what do you mean exactly? Do you basically want them to appear as completely unstyled inputs?