That's a bit more in depth, but to answer your question generically first:
RPM's (and other's for that matter) choose to install it's components to generally accepted default locations. For the libs that'd be /usr/lib for the binary it's usually /usr/bin /usr/local/bin and/or /usr/sbin /usr/local/sbin (super user). But it really shouldn't matter because the location tends to be located within your $PATH variable. What this is, is a set of directories that are setup for you that are searched when the binary is typed into a run box, or into a terminal (command line).
So, to execute said binary, you'd either open up a run box in a desktop environment and type the name of the program:
mysql (just an example, this should only work for X applcations in reality)
And the program will run, OR
open up a terminal, and type the same thing to start the program from there. There is no need to know the location of all the files that were installed from running the RPM.
That said, MySQL is different
Normally you don't run mysql, but rather a front end for it. If you are experienced enough or have a set of instructions to pass to MySQL via the command line, that's fine. You'll need to get into mysql first, so open up a command line and type:
mysql -u username -p
And it should prompt you for the username's password. By default I believe the only user setup will be the root user, and this user has no password, so set one up immediately. You'll need to have the mysqld (daemon) running to connect to it, and all of this AND MORE should be covered in the documentation at www.mysql.com
and/or your distro's documentation if that's where you got the RPM from