How does one do on-line database backups?

Each tablespace that needs to be backed-up must be switched into backup mode before copying the files out to secondary storage (tapes).
Look at this simple example.

ALTER TABLESPACE xyz BEGIN BACKUP;
! cp xyfFile1 /backupDir/
ALTER TABLESPACE xyz END BACKUP;

It is better to backup tablespace for tablespace than to put all tablespaces in backup mode. Backing them up separately incurs less overhead. When done, remember to backup your control files.
Look at this example:

ALTER SYSTEM SWITCH LOGFILE; -- Force log switch to update control file headers
ALTER DATABASE BACKUP CONTROLFILE TO '/backupDir/control.dbf';

NOTE: Do not run on-line backups during peak processing periods. Oracle will write complete database blocks instead of the normal deltas to redo log files while in backup mode. This will lead to excessive database archiving and even database freezes.