Going by your question, I will like to review what I believe you did thus far:

• You stopped mysql on the Master
• You copied Master's /var/lib/mysql to the Slave's /var/lib/mysql
• I surmise the binlogs on the Master were copied as well

Look at the Slave's last binlog. From the question, it should be

• mydbm1-bin.008524
• Filesize 1330529

Believe it or not, you have to do a few things:

1) On the Master, create a replication user like this:

GRANT REPLICATION SLAVE,REPLICATION CLIENT
ON *.* TO replicator@'%'
IDENTIFIED BY 'r3plic4t0R';

2) Make /var/lib/mysql on the Slave owned by mysql user

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

3) Make sure Master's server_id is explicitly set in my.cnf

[mysqld]
server_id = 1

4) Make sure Slave's server_id is explicitly set in my.cnf

[mysqld]
server_id = 2

5) Startup mysql on the Slave

service mysql start

6) Setup replication by running this on the Slave

CHANGE MASTER TO
MASTER_HOST='IPAddressOfMaster',
MASTER_PORT=3306,
MASTER_USER='replicator',
MASTER_PASSWORD='r3plic4t0R',
MASTER_LOG_FILE='mydbm1-bin.008524',
MASTER_LOG_POS=1330529;
START SLAVE;
SELECT SLEEP(5);
SHOW SLAVE STATUS\G

You will see something like this:

mysql> show slave status\G
*************************** 1. row ***************************
             Slave_IO_State: Waiting for master to send event
                Master_Host: 10.48.20.253
                Master_User: replicant
                Master_Port: 3306
              Connect_Retry: 60
            Master_Log_File: mysql-bin.000254
        Read_Master_Log_Pos: 858190247
             Relay_Log_File: relay-bin.066069
              Relay_Log_Pos: 873918
      Relay_Master_Log_File: mysql-bin.000254
           Slave_IO_Running: Yes
          Slave_SQL_Running: Yes
            Replicate_Do_DB:
        Replicate_Ignore_DB:
         Replicate_Do_Table:
     Replicate_Ignore_Table:
    Replicate_Wild_Do_Table:
Replicate_Wild_Ignore_Table:
                 Last_Errno: 0
                 Last_Error:
               Skip_Counter: 0
        Exec_Master_Log_Pos: 858190247
            Relay_Log_Space: 873772
            Until_Condition: None
             Until_Log_File:
              Until_Log_Pos: 0
         Master_SSL_Allowed: No
         Master_SSL_CA_File:
         Master_SSL_CA_Path:
            Master_SSL_Cert:
          Master_SSL_Cipher:
             Master_SSL_Key:
      Seconds_Behind_Master: 0
1 row in set (0.00 sec)

If Slave_IO_Running and Slave_SQL_Running are both Yes, CONGRATULATIONS !!!

I already answered a post back on Feb 06, 2012 ( How to setup replication(Master/slave) in MySQL 5.5.20? ) with essentially the same steps.

I wanted to add additional posts I made for setting up Circular Replication should you decide to setup the two DB servers as Master/Master

• Sep 24, 2012 : Setting up MySQL circular replication in existing replication topology?
• May 07, 2012 : Setting Circular Replication in mysql

The MySQL replication process works like follow :

• Transactions are executed on the Master
• All transactions are written in Binary Logs files (mysql-bin.xxxxx) as "event" on the Master
• On a Slave, two threads are dedicated to the replication process
  • The I/O thread reads the Master Binary Logs events and writes them to the relay log in local (mysqld-relay-bin.xxxxx)
  • The SQL thread reads the Relay Log events and executes them on the Slave

In the SHOW SLAVE STATUS\G output the important info are:

What is the current Master position?

• Master_Log_File: The current Binary Log of the Master
• Read_Master_Log_Pos: The current Binary Log position of the Master

What is the current Slave position?

• Relay_Log_File: The current Relay Log of the Slave
• Relay_Log_Pos: The current Relay Log position of the Slave

What is the current Slave position regarding to the Master's Binary Logs?

• Relay_Master_Log_File: The Binary Log (on the master) which corresponding to the actual position of the slave
• Exec_Master_Log_Pos: The Binary Log position (on the master) which corresponding to the actual position of the slave

Now, if you don't use the Binary Logs on Slaves (for point in time recovery or chained replication) you can disable it and remove them:

log_bin = 0

To purge your binary logs, use:

PURGE BINARY LOGS;

Note regarding log-slave-updates: by default if you enable Binary Logs on Slave, the Slave will only writes events executed on the Slave directly, none of the events coming from its Master will be written in the Slave's Binary Logs. If you want to setup a chained replication (M -> S/M -> S), you need to tell the Slave to logs the Master events on its Binary Logs to replicate them on its own Slaves. This options is log-slave-updates.

If you need to enable Binary Logs on Slave the command to see the curent position of the Slave´s Binary Logs is SHOW MATSER STATUS; you will see the position coresponding to your files on your directory (on slave).

Note on Binary Logs managment: Do not forget to set a "purge strategy" for your Binary Logs if you don't want to saturate your disks. The simplest way is to use the expire_logs_days variable which tell to MySQL to purge its Binary Logs older than this variable.

I hope I was clear...

Best Regards