Before iOS7 all you had to do was to press the Home button twice and Spotlight search used to popup on the screen. But in iOS7 this does not work and you end up struggling on, how to search apps and mails in iOS7 using spotlight search.
On iOS7 in order to use spotlight search, you need to pull your screen down, by swiping down at any location on the screen. This will reveal spotlight search option at the top of the screen.
Just make sure that you are not touching the top of the screen while swiping down otherwise it will open something else. 😉