There are many apps that you can download to a mobile device in order to scan a document or picture with your smartphone or tablet. Scroll down for suggested apps, and see the links at the bottom of the page. If you don't want to use one of these, you can always take a picture using your phone's camera and store your document as an image.
Apple's own document scanner is inside the Notes app: under the More button (or '+' sign), tap "Scan Document". You can mark up the scan or convert it to a PDF.
For an Android device, you can consider using Google Drive. It comes with a scanning tool built-in, which can also convert scans to PDF documents.
Evernote Scannable for iOS can be used for all Apple devices (iPhones and iPads) and works great with Evernote.
Some other apps include Dropbox for iOS and Android, Scanbot for iOS or CanScanner for iOS and Android. All of these basic apps are free but can be upgraded for more features.
