Every database has its own set of tools, no matter if you are on a Mac or a pc. Besides the administrative tools that come out of the box with the database, you can also download free or commercial additional tools.
For example, Oracle has a web based tool that comes and installs with the database called Enterprise Manager (besides the command line tools), but also offers the SQL Developer which you can download free. There are also commercial tools like Toad and navicat.
For MySQL, by installing it you'll be able to perform managing tasks by command line. But there are also free great tools like phpmyadmin and MySQL workbench. And you'll find even more if you search for it.
Currently I am taking a database class and was told MySQL makes it easier to run SQL commands so I thought I would try that. How do I install this? Is it easier than just using Access to run SQL commands?
Access (assuming you mean MS Office Access) uses MS-SQL, iirc.
MySQL is a server package you can install on most computers, it has a basic interface. There is a manager application called phpmyadmin, but that requires, in addition, a webserver with PHP extensions installed.
MySQL can be downloaded from here: http://dev.mysql.com/downloads/mysql/
Installation instructions are available from here: http://dev.mysql.com/doc/refman/5.5/en/macosx-installation.html
For a GUI download MySQL Workbench from here: http://www.mysql.com/downloads/workbench/
once I master SQL the old fashioned way through Access
I'm on a PC right now so I can't double check this but you should simply be able to type in sqlite3 into the command line and it'll enter interactive mode.
Hahahaha. Trust me that Access is anything but the old fashioned way.
Yeap, SQLite is installed by default. On Mac OS X 10.7.2 is version 3.7.5.