Method 1:Through SQL command prompt.

SQL> select dbid from v$database;

DBID
----------
3764293269


Method 2:Through RMAN

[oracle@canada ~]$ rman target =/

Recovery Manager: Release 11.2.0.1.0 - Production on Fri Dec 14 16:41:00 2012

Copyright (c) 1982, 2009, Oracle and/or its affiliates. All rights reserved.

connected to target database: DELL (DBID=3764293269)

RMAN>

Method 3: By Generating Trace Files

SQL> startup nomount
SQL> alter session set tracefile_identifier = myoradump;


SQL> alter system dump datafile '/u01/app/oracle/oradata/dell/system01.dbf' block min 1 block max 10;

In user_dump_test find trace file "myoradump" in that search "Db ID"

Start dump data block from file /u01/app/oracle/oradata/dell/system01.dbf minblk 1 maxblk 10
V10 STYLE FILE HEADER:
Compatibility Vsn = 186646528=0xb200000
Db ID=3764293269=0xe05e8e95, Db Name='DELL'
Activation ID=0=0x0
Control Seq=659=0x293, File size=85760=0x14f00
File Number=1, Blksiz=8192, File Type=3 DATA




Same command can be used for log and archived log files

SQL> alter system dump logfile" "