Adding a Dropdown to Filter my Search

I’ve searched this and it seems like I am only finding those who already know how to do it. What I’m asking for is really help on PHP than wordpress.

I’d like to have a dropdown next to my search box on all pages (so, part of my searchform.php) that searches only subpages of a particular parent page. So the drop down would look like something like this: (I’m going to try to space this out so you get an idea… ?? –You might see a lot of quick follow up edits–

-Entire Site ||Search Box|| SUBMIT
-Photoshop
-Windows

(it kinda looks like it) ?? My question tho is how to do this in php. It looks like the searchform.php sends a GET to the homepage url, and I gather that to do a search you just add ?s= and then the text you want to search. I feel like I don’t know what I don’t know yet about search forms…