Well the search input is like my screenshot above, and the result page is like that (standard /?=text WP search URL generated by default search template with default query and simple query template including post title):
I actually transformed the input to button/modal yesterday because it was easier to deal with responsive header 
As for linking to a more complex results page with filters, there are different ways to do it.
One common way for me seems to be using a similar form with multiple inputs which convert to parameters in result page URL, then on this page you need to get the URL parameters to feed the query.
Haven’t played with Cwicly filters yet so I can’t tell about a Cwicly dedicated solution.