Dragon Dictation, a simple speech-to-text app that is free on iOS, is probably the best known. On the left of its main page is a list of Notes you've previously entered; on the right is a larger section where you enter or view text inside notes. At the top of the main section is a red Record button.
The app records for as long as necessary, showing the audio level of your voice as a graph at the bottom of the screen. Tapping anywhere on the screen turns off recording, or you can adjust the app to automatically detect when you've stopped speaking.
The app sends a digital sample of your speech over the internet to do the speech recognition, so it requires a wireless connection. But this process is speedy, and the app soon displays your transcribed text in the main window. You may be surprised at how accurate it is.
For example, it successfully transcribed, "I read the red book," even though "read" and "red" are pronounced the same. Fixing or editing text is easy. Tap on a word, and the app gives you the option to delete it or bring up an on-screen keyboard for manual corrections.
When you are satisfied, the app can send the text by e-mail or share it on Facebook or as a Twitter post. Although the app works very well, I've found that using a plug-in microphone with it provides the best speech recognition.
Listnote Speech/Text Notepad is a similar Android app, available as an ad-supported free download. Like Dragon, the app's main interface revolves around your list of previous notes. These can be organised by categories. To create a speech note, you tap on the large Speech Recognition button at the top of the app, then speak. Translated text quickly appears in the relevant space in a new Note section on the screen.
If the text wasn't quite what you said, tap on the arrow icon near the text and select from a short list of other guesses. Alternatively, you can edit the text manually by long-pressing on it.