Hot backup when Oracle Database is up

There are two ways. The preferred way with Oracle's databases today is to use RMAN. The following will perform a hot backup using RMAN:

rman target /
run {
   allocate channel t1 type disk format '/dir/%d_FULL_%U ';
   backup database;
}

Alternatively, you can place a tablespace in hot backup mode by the following:

ALTER TABLESPACE ts_name BEGIN BACKUP;

Once a tablespace is in backup mode, you can use any OS utility to copy the tablespace's datafiles to the backup location. Once the tablespace backup is done, end the tablespace backup:

ALTER TABLESPACE ts_name END BACKUP;

Repeat for each tablespace.

Read more about hot backups and other backup and recovery issues in our Database storage management All-in-One Guide.