Connecting remote MySQL database to local MySQL database?
There are 3 methods to set this up
METHOD #1 : MySQL Replication
Setup MySQL Replication where the Slave has this option
replicate_do_table=mydb.mytable

Then, any DML (INSERT, UPDATE, DELETE) or DDL (ALTER TABLE) you execute will go immediately to serverB. This makes Method #1 is the fastest and most granular approach.
METHOD #2 : Copying the table to the other server
Rather than rehash, Here is an earlier post I did May 31, 2011 for this method : How do you copy a table from MySqlServer_A to MySqlServer_B?
METHOD #3 : FEDERATED Table (MyISAM Only)
Suppose mytable on serverA looks like this
CREATE TABLE mydb.mytable
(
...
) ENGINE=MyISAM;

You can a mapping of the target table in serverB by running this on serverA like this
CREATE TABLE mydb.mytable_remote LIKE mytable;
ALTER TABLE mydb.mytable_remote ENGINE=FEDERATED
CONNECTION='mysql://username:password@serverB/mydb/mytable';

I wrote an earlier post back on Jan 4, 2012 : fetching externally hosted db&#39;s table from within the local mysql server
Then you would have to bulk copy everything in serverA to serverB running the following on serverA:
INSERT IGNORE INTO mydb.mytable_remote SELECT * FROM mydb.mytable;