I have a DB table that has a auto increment integer primary key, if I insert a new record into it by SQL statement "INSERT INTO...", how can I get the integer primary key value of that newly created record?

For this purpose, you can use mysql_insert_id().
It returns the value generated for an auto_increment column by the previous INSERT or UPDATE statement.
Full documentation to be found in the mySQL manual that can be downloaded from www.mysql.com.

hi

The answer to your problem is very simple.
you do one thing whenever you give INSERT statement keep that field blank.

when you keep it blank mysql qill automatically increase its value in database.

Thanks binkie. Another question is there may be more than 1 people inserting new records into this table concurrently, so any more things need to do?

mySQL keeps track of more people doing simultaneous inserts. That's why you should NOT use a SELECT MAX(KEY) FROM TABLE because someone else may have inserted a record just after you, and will get the wrong key value.
mySQL links your particular session to the actions that you have executed. By doing so, mysql_insert_id() will return YOUR inserted key, no matter how many people are inserting at that moment.