I am such an idiot, but I can't figure out how to attach this pump head to my Schrader valve. The lever doesn't seem to flip up??
That's a quick chuck commonly found at gas stations. There's no locking mechanism.
You just push the quick chuck head firmly onto the schrader valve and squeeze the air release. Hand pressure alone keeps the valve seated against the chuck. With car tires (see photo below) it's easy as the schrader valve is solidly affixed to the tire rim. With bicycle tires, it's a bit tricky as the schrader valve isn't fixed and can push into the rim, so sometimes you have to gently push or hold the other side of the schrader valve with your other hand to steady it.
Note that it's VERY easy to overinflate a bicycle tire with these car inflators as they commonly don't have a max pressure setting. I've blown a tire off a rim using a gasoline station quick chuck. So be very careful and fill using only short, quick spurts of air.