First, with Windows, you need to be connected as the Administrator account which installed the Oracle software to use the '/' connection shortcut.
Now, to backup a tablespace with RMAN the command is simple:
RMAN> backup tablespace hr tag hr_backup;
Presuming the database is in ARCHIVELOG mode you can backup the tablespace while the database is running. If the database is in NOARCHIVELOG mode then you must shutdown the database, start it up in mount mode and then backup the tablespace:
RMAN> shutdown
database closed
database dismounted
Oracle instance shut down
RMAN> startup mount
connected to target database (not started)
Oracle instance started
database mounted
Total System Global Area 753299456 bytes
Fixed Size 1387240 bytes
Variable Size 213910808 bytes
Database Buffers 532676608 bytes
Redo Buffers 5324800 bytes
RMAN> backup tablespace hr tag hr_bkp;
Starting backup at 04-DEC-12
allocated channel: ORA_DISK_1
channel ORA_DISK_1: SID=63 device type=DISK
channel ORA_DISK_1: starting full datafile backup set
channel ORA_DISK_1: specifying datafile(s) in backup set
input datafile file number=00007 name=C:\ORADB\ORADATA\SMEDLEY\HR01.DBF
channel ORA_DISK_1: starting piece 1 at 04-DEC-12
channel ORA_DISK_1: finished piece 1 at 04-DEC-12
piece handle=C:\ORADB\FLASH_RECOVERY_AREA\SMEDLEY\BACKUPSET\2012_12_04\O1_MF_NNNDF_HR_BKP_8CW68821_.BKP tag=HR_BKP comment=NONE
channel ORA_DISK_1: backup set complete, elapsed time: 00:00:03
Finished backup at 04-DEC-12
RMAN>
How you can open the database and get back to work:
RMAN> sql "alter database open";
sql statement: alter database open
RMAN>
David Fitzjarrell