Connecting to Oracle SQL Developer locally on Mac?
SQL Developer doesn't come with an Oracle database, it is a client application. You can't "connect to SQL Developer", you use SQL Developer to connect to an existing database.

There are no supported editions of Oracle database for Mac OS X at this time, the latest that was available was 10gR2. You'll need to set one up in a VM on your machine (Windows or Linux, using the Oracle XE edition seems like it would fit your need), or see if you can somehow connect to your lab databases (possibly via a VPN to your school if they have that available).