When I try to run mysql it says...

[root@pc2 /]# mysql
ERROR 2002: Can't connect to local MySQL server through socket
'/tmp/mysql.sock' (111)
[root@pc2 /]#

I think I need some suggesion or hint...

Is mysqld running? Check the process table (ps -A).

It does indeed sound like you don't have mysql running, Here's how to make sure it's set up properly :

Further notes on mysql:
From an initial install the databases have to be created for the
users, typing:
mysql_install_db

should create the tables but then the owner for these files needs to be
changed to 'mysql' instead of root.
The files in question are in /var/lib/mysql and the owner and group both
need to be set to mysql ie:

cd var/lib/mysql
chown -R mysql:mysql mysql

Mysql can then be started:
safe_mysqld &

and mysqladmin used to change the root password:

mysqladmin -u root password 'new-password'

Other users can then be setup on mysql by logging in and then using:

grant all on * to fred identified by 'pass' with grant option;
This would grant all privileges on all db's to fred

mysqld is not running....when I give ps -A it says..

[root@pc2 /]# ps -A
PID TTY TIME CMD
1 ? 00:00:49 init
2 ? 00:00:00 keventd
3 ? 00:00:00 kapmd
4 ? 00:00:00 ksoftirqd_CPU0
9 ? 00:00:00 bdflush
5 ? 00:00:00 kswapd
6 ? 00:00:00 kscand/DMA
7 ? 00:00:00 kscand/Normal
8 ? 00:00:00 kscand/HighMem
10 ? 00:00:00 kupdated
11 ? 00:00:00 mdrecoveryd
70 ? 00:00:00 khubd
2160 ? 00:00:00 syslogd
2164 ? 00:00:00 klogd
2190 ? 00:00:00 portmap
2209 ? 00:00:00 rpc.statd
2278 ? 00:00:00 apmd
2316 ? 00:00:00 identd
2340 ? 00:00:00 snmpd
2350 ? 00:00:00 named
2362 ? 00:00:00 routed
2372 ? 00:00:00 sshd
2386 ? 00:00:00 xinetd
2398 ? 00:00:00 ntpd
2414 ? 00:00:00 nwserv
2423 ? 00:00:00 nwbind
2429 ? 00:00:00 rpc.rquotad
2434 ? 00:00:00 nfsd
2435 ? 00:00:00 nfsd
2436 ? 00:00:00 nfsd
2437 ? 00:00:00 nfsd
2438 ? 00:00:00 nfsd
2439 ? 00:00:00 nfsd
2440 ? 00:00:00 nfsd
2441 ? 00:00:00 nfsd
2444 ? 00:00:00 lockd
2445 ? 00:00:00 rpciod
2449 ? 00:00:00 rpc.mountd
2458 ? 00:00:00 rpc.rstatd
2468 ? 00:00:00 vsftpd
2499 ? 00:00:00 ncpserv
2506 ? 00:00:00 netdump-server
2525 ? 00:00:00 sendmail
2534 ? 00:00:00 sendmail
2544 ? 00:00:01 spamd
2555 ? 00:00:00 scsi_eh_0
2560 ? 00:00:00 iscsid
2568 ? 00:00:00 gpm
2579 ? 00:00:00 httpd
2630 ? 00:00:00 postmaster
2632 ? 00:00:00 postmaster
2633 ? 00:00:00 postmaster
2647 ? 00:00:00 cannaserver
2658 ? 00:00:00 crond
2666 ? 00:00:00 httpd
2667 ? 00:00:00 httpd
2668 ? 00:00:00 httpd
2669 ? 00:00:00 httpd
2670 ? 00:00:00 httpd
2671 ? 00:00:00 httpd
2672 ? 00:00:00 httpd
2673 ? 00:00:00 httpd
2677 ? 00:00:00 cupsd
2721 ? 00:00:00 jserver
2733 ? 00:00:00 squid
2735 ? 00:00:00 squid
2737 ? 00:00:00 unlinkd
2815 ? 00:00:00 xfs
2836 ? 00:00:00 atalkd
2837 ? 00:00:00 smbd
2841 ? 00:00:00 nmbd
2850 ? 00:00:00 winbindd
2859 ? 00:00:00 anacron
2868 ? 00:00:00 atd
2909 ? 00:00:00 login
2910 tty2 00:00:00 mingetty
2911 tty3 00:00:00 mingetty
2912 tty4 00:00:00 mingetty
2913 tty5 00:00:00 mingetty
2914 tty6 00:00:00 mingetty
2915 ? 00:00:00 sshd
2917 pts/0 00:00:00 bash
2969 ? 00:00:00 papd
2973 ? 00:00:00 afpd
2976 tty1 00:00:00 bash
3031 pts/0 00:00:00 ps
[root@pc2 /]#

when I give mysql_install_db it says...

[root@pc2 /]# mysql_install_db
Installing all prepared tables
040411 6:34:47 /usr/local/libexec/mysqld: Shutdown Complete


To start mysqld at boot time you have to copy support-files/mysql.server
to the right place for your system

PLEASE REMEMBER TO SET A PASSWORD FOR THE MySQL root USER !
This is done with:
/usr/local/bin/mysqladmin -u root password 'new-password'
/usr/local/bin/mysqladmin -u root -h pc2.dns2.com password 'new-password'
See the manual for more instructions.

NOTE: If you are upgrading from a MySQL <= 3.22.10 you should run
the /usr/local/bin/mysql_fix_privilege_tables. Otherwise you will not be
able to use the new GRANT command!

You can start the MySQL daemon with:
cd /usr/local ; /usr/local/bin/safe_mysqld &

You can test the MySQL daemon with the benchmarks in the 'sql-bench' directory:
cd sql-bench ; run-all-tests

Please report any problems with the /usr/local/bin/mysqlbug script!

The latest information about MySQL is available on the web at
http://www.mysql.com
Support MySQL by buying support/licenses at https://order.mysql.com

[root@pc2 /]#

I am very much new to use mysql at linux....

Well done, that's the first step out of the way, now continue and follow my instructions from earlier, you'll be fine.

Ade

I think my rpm and tar file is creating problem for me..

can you tell me how can I uninstall any tar file..

I mean I have downloaded mysql-3.23.56.tar.gz then untar it and run ./configure, make and make install ...

but before that I did not remove the rpm package which were already installed...

I think these two installation is creating problem for me...

I am trying one thing which says...

[root@pc4 /]# rpm -evv mysql
Segmentation fault
[root@pc4 /]#

what is that segmentation fault...

or can you tell me that how can I uninstall the tar file installation..

go back to your source folder and type :

make uninstall