You will need to have downloaded and installed the latest database driver Connector/J 5.1 [1] includes support for the latest JDBC functionality.
Open the Omniscope Database Connection wizard under File > Connect to database. Choose the generic "JDBC data source (advanced)" option on the first page.
Follow through the rest of the Database Connection wizard as usual, specifying a username and password, choosing a table, and optionally customising the SQL query.
Links:
[1] http://dev.mysql.com/downloads/connector/j/5.1.html
[2] http://dev.mysql.com/doc/refman/5.0/en/connector-j.html