Your best bet is to research "digital audio sampling theory". Some brave soul could possibly spend time loading all of the current research data into a stack answer, but it would duplicate a lot of really good reading material that is currently out there.
You are very close with your current observations, but you should take into account that an analogue audio signal is basically 'alternating current', in that the changing sound pressure that reaches the microphone capsule is made up of areas of compression and decompression of the air around the capsule. Consequently, the voltage that is generated by the capsule is both positive and negative depending on the direction of excursion of the capsule. You will likely see a "zero" voltage level being the 'centre' of the signal, and the signal varying both positively and negatively around this 'centre'.
The 'number' that is used to represent the sampled voltage will depend very much on the format of the samples. You could use 'signed integers', 'unsigned integers' or 'floating point'.
Floating point is easiest to understand as it is by nature a real number with a range of -1.0 through 1.0 and every sample will lie somewhere in this range.
The signed integer range will depend entirely on the bit resolution of the sample. For instance a signed 8-bit integer will lie on a range of -127 through +127 and an unsigned 8-bit integer will lie on a range of 0 through 255.
When passing this data through an FFT library, you will need to use similar numeric encoding, or pass the data through a transformation function in order to adapt it to a format that the FFT library will want to work with.