What really happens when you make an internet phone call?

Whenever you make an internet phone call, your voice goes through several processes:
When you talk into the receiver of your phone an analog voice signal is sent to your internet VoIP phone adapter better known as an ATA (analog telephone adapter). The adapter then converts your analog voice signal into a digital voice signal through a process call Analog-to-Digital Conversion (ADC) to prepare for transmission across the internet.
The next step in preparing your voice for an internet phone call is to compress the digital bits created by the ADC conversion into a standard format. An Internet phone provider uses a codec, which stands for coder-decoder, in order to compress the digital audio signal into packets of data. This process is essential for internet phone service to work properly. The G.729A is the most commonly used codec among internet phone providers for transmitting your voice across the internet. Some other commonly used codecs and their sampling rates are:
Codec Definition Standard Sampling Rate Uses
PCM Pulse Code Modulation ITU-T G.711 64Kbps Standard Telephone Line
CS-ACELP conjugate-structure algebraic-code-excited linear prediction ITU-T G.729 and G.729a 8Kbps Internet Phone Service
ACELP algebraic-code-excited linear prediction ITU-T G.723.1 5.3Kbps True Voice
ADPCM Adaptive differential PCM ITU-T G.726 40Kbps Variation of PCM
After your voice is compressed into data it is then encapsulated inside of IP packets before being routed across the internet. The challenge forinternet phone service is knowing where to route these “voice packets”. A device known as known as a soft switch is used to ensure these “voice packets” are routed to the proper destination. The soft switches act as a big database that maps a static phone number to a dynamic IP address to ensure you are able to make and receive calls across the internet. Without soft switches internet phone service wouldn’t be possible.
In order for someone to actually connect to you on the other end of an internet phone call, everything between you and the person on the other end must work together smoothly. Your voice is transmitted by using several protocols. Protocols define ways in which codecs connect to each other and with the internet. Internet phone service typically uses UDP (user datagram protocol) for transmission in combination with several other protocols. H.323 is the most widely used protocol for voice transmission however it wasn’t designed with internet phone service in mind. As you can see in the table below, H.323 is quite a large suite of protocols that was originally developed for video conferencing but has evolved and is widely used for tons of different applications.
H.323 Protocol Suite
Video Audio Data Transport
H.261
H.263 G.711
G.722
G.723.1
G.728
G.729 T.122
T.124
T.125
T.126
T.127 H.225
H.235
H.245
H.450.1
H.450.2 
H.450.3
RTP
X.224.0
Since H.323 wasn’t thinking of transmitting voice for internet VoIP phone calls, several other protocols have been developed that are smaller and more streamlined specifically for internet phone service. SIP or session initiation protocol was created for setting up, creating, and terminating an internet VoIP phone call. MGCP or media gateway control protocol is another protocol that is used with internet calls and was developed mainly to control features like call waiting. For an in-depth explanation of how these protocols work visit: VoIP Protocols
Finally, your IP packet arrives at the proper destination, it goes through the reverse process as described above so the person at the other end is able to hear your voice. Everything takes place in real time so any missing packets or delays are so small they are virtually undetectable by the human ear.
The the technical internet phone service diagram below provides a high level overview of how your voice travels across the internet to reach it's destination and connect to the other end.

The dotted line represents the path of your voice as it travels to its destination. The call coming from your internet VoIP phone first travels through your internet service provider "ISP" before passing to your internet phone provider's network. Depending on who you are calling will determine whether or not your call is routed to the cellular network or to the traditional public switched telephone network "PSTN". The person on the other end then hears a ring and you are connected. This process simply happens in reverse when somone is calling you.