In previous versions of iOS, Spotlight -- Apple's search utility -- has always been available by going to the first home screen, then swiping right. In iOS 7, Spotlight is now available on every home screen. Here are two short videos to show you how to use Spotlight in iOS 7, and also how to change the order of search results.
To access Spotlight, simply swipe down on your home screen. Some sites have been mentioning that you need to be in the top row of apps or folders before beginning the swipe -- that's untrue, as you can be anywhere on the screen to begin the swipe. Here's the video (which can be resized to full screen, by the way):
Once you've swiped, Spotlight quickly fades into view. Type in your search phrase, and Spotlight provides a list of all eligible apps, contacts, music, podcasts, mail, events, messages, videos, audiobooks, notes, voice memos and reminders that contain the search phrase and are stored on your device.
I like to use Spotlight as an app launcher, so I wasn't initially happy to find that applications were showing up in the search results after contacts. A quick look at Settings > General > Spotlight Search revealed a way to order the search results so that applications were first in the list -- you just tap on the "hamburger" (three horizontal lines) next to the search item, and drag the item up or down on the list. Individual items can also be unchecked with a tap to remove them from the Spotlight search results.