As I'm sure runrig knows there are 3 basic ways to connect via ODBC. DSN=yourdsn, FILEDSN=a_file_with_Attributes and so called DSN-less connection with DRIVER=xxx. On Windows you can also add odbc_driver_complete which may throw a dialogue (if you have a window handle) to complete the connection attributes via a dialogue (you might use this to prompt for username/password etc)
One really useful thing is odbc_out_connect_string which you can use after any successful connect to find out the connection string you can use to connect to this data source again in the future. This is typically what MS Access (and other apps) use to store a connection string after you've filled in a dialog to connect to an ODBC driver.