For most of this section we'll assume, for simplicity, that you are the sender of messages and someone else is the recipient. In practice, of course, you're likely to be sending messages to each other, and so everything we describe is actually happening in both directions.
Throughout this explanation, we have taken care to say "your SSL software does so-and-so" not "you do so-and-so". This is partly to emphasize that all the detailed work is done by the software - as a user, or even as a programmer, of SSL-enabled software you generally just set options. It is also to emphasize that you must keep your computer secure, with such things as login passwords. If someone else can use your SSL software in your place, obviously all security is lost.