The modem checks for a
dial tone. The modem dials the phone number. The other modem answers
the call and they both do a process called "handshaking".
This is where the modems will attempt to communicate at the same
speed, with the same protocols. They do this communication over what
is called a Carrier Signal. Under most circumstances 56k modems will
first try to negotiate a V.90 connection, then a K56Flex connection
and if both those fail they will do V.34. The modems will also try to
negotiate the highest speed possible and then go down to a speed that
they can communicate at.
During the connection
modems can and often will change speeds depending upon the phone line
conditions. They do this through renegotiations and retraining. If
modems renegotiate (also called fall-back and fall-forward) they
simply will change speeds. If they retrain they will do a complete
re-handshake and form a new speed. Most modems have a setting that
tells them to do a full retrain after a certain number of
renegotiations and to disconnect after a certain number of retrains.
It is worth noting that modems are often poor at determining what
speed they should communicate at to have a reliable connection.