Q:

How to use Speech Recognition inside the iOS SDK? 

I know that there is no public API for the SIRI-Services,
but is there an API for simple Speech-Recognition?   So if I have a textfield and the user taps onto that textfield, a keyboard with the typically microphone button appears and if he pressed it the speech get recognized and transformed into a string object?  Or is this button maybe presented by default? 

A:

There are many libraries availble.  You can use any of them. 

openears // This is the best library
VocalKit (Deprecated for open ears)
TTS 
ispeech (Not free)

Hope it helps you. 
NOTE: 
if you download openears (which contains a sample project called "OpenEarsSampleApp") @efimovD mentions this

Check the code in view controller and you will see an array with
  possible commands.  This thing detects commands!  Not some talk.  It
  listens and tries to compare what you've said with the words from
  array

