All database interactions are conducted via the SQLManager class. A full list of its methods is beyond the scope of this document, but its primary purpose is to allow for different DBMSes (e.g., MySQL, Postgres, etc) without altering PHP code. In general, its methods correspond to PHP's MySQL functions with the "mysql_" removed (e.g., query(), fetch_row(), num_rows(), error(), etc). Learning all the classes' methods is encouraged but probably overkill when just getting started.
Request a database connection via the FannieDB class. It contains a static method, get($db_name [string]) where $db_name is the name of a database. The global configuration variables $FANNIE_OP_DB, $FANNIE_TRANS_DB, and $FANNIE_ARCHIVE_DB contain the names of Fannie's three default databases. These are user-customizable so don't hardcode common defaults like "core_op" or "is4c_trans".
If your plugin needs additional tables and/or views, include a database name option in the plugins' settings so the user has the option of keeping the plugins' tables/views in a separate database. This reduces the chances of running into name problems where two plugins want to use the same name for a table/view and makes it easier for the user to manage data related to the plugin. Deleting tables or views when the plugin is disabled is generally a bad idea unless that data can be easily recreated. Losing data due to a mistaken configuration change is bad. Clearly keeping the plugins' tables/views separate makes it more reasonable for the user to decide what is safe to manually delete.