Let's say you are interested in frequencies up to 500 Hz (about 1 octave above middle C on a piano). So before you digitize a signal you have to decide what the frequencies of interest are, and remove all higher frequencies with a filter. If you sample a high frequency signal with a low frequency sample clock, it will appear 'aliased' - it wil show up in your output as something completely different. Note - it's not just 'that you are interested in', but 'that is present'. There is a formal theorem called 'Nyquist's Theorem' that states that you have to sample at 2x the highest frequency that is present in your signal. In order to detect a high frequency, you need to sample the signal 'faster than it is changing'. A sound signal contains many different frequencies - think of them as keys on the piano.

The second point, 'choosing the sampling rate', is actually very important.

It sounds from your tag that you are trying to do that inside an Android device - in which case I wonder how you intend to move the digital signal to the Arduino (over USB?). Without more information about the hardware you are using, there's not a lot to add here. For example, if you have a microphone as your sound input source, you will need to amplify the signal (and maybe add some automatic gain control) before feeding it into an ADC (analog to digital converter) that has a 5 V input range, since the microphone may have an output in the mV range. Items (1) and (3) are related, since you need to know how you are going to digitize the signal before you can choose the right amplitude. Digitizing and storing the data for later processing.Getting the signal to the right amplitude.This breaks down into three separate sub problems:

Problem #1: converting audio signal into a stream of numbers This means that you need to convert them into a stream of numbers first. Presumably, your audio signals are 'coming from somewhere' - i.e. I am going to help you think through the problem - asking yourself the right questions is essential to get any answers. You are asking a very fuzzy question: 'How should I build audio signals which ultimately can be turned into FFTs and the Arduino can analyse the same using the library and I can actuate anything?'.

Arduino cw decoder fft