when you type 'mysql' at the command line, you're using the utility 'mysql' which allows you to access the database...
the reason it wasn't working when you tried:
shell>cd /usr/local/mysql/
shell>mysql -u root -p
is that this utility is in the bin folder (hence: /usr/local/mysql/bin/mysql), and not in the mysql folder - thus the 'command not found' message...
you can therefore, get it to work by making a small change:
shell>cd /usr/local/mysql/bin/
shell>mysql -u root -p
as for how to modify $path, you can find some info here (i haven't done that myself, so i can't give you much information):
http://www.entropy.ch/phpbb2/viewtopic.php?p=237&;