There are many ways to record high-quality audio (for interviews, etc.) on your smartphone. Here are a few listed below.
The simplest way is using the internal “Voice Memos” app – written instructions here or the official Apple support page here. Or Watch this video for iOS 7 Here:
If you don’t like that one, here is a list of 9 more apps you could try.
Android does not have a built-in app (some of the companies like Samsung include them)
The most popular is the Audio Recorder by Sony which you can download here
The Sony Audio Recorder is pretty intuitive, but you can also follow this quick video tutorial here:
If you don’t like that one, here is a list Good list of 10 Apps for recording