If the same connection/user, you should be able to do something like:
$connx = mysql_connect('localhost', 'dbuser', 'dppassword') or die(mysql_error());
$sql = "
INSERT INTO database2.table_name (fld1, fld2, fld3)
SELECT fld1, fld2, fld3 FROM database1.table_name
$result = mysql_query($sql) or die(mysql_error());
If separate connections/users are required, then you'd either have to query the first DB, save the results into an array, then use that array for inserting into the 2nd DB; or perhaps you could use the DBMS command line functions to create a SQL file, then load that file into the second DB.
"Please give us a simple answer, so that we don't have to think, because if we think, we might find answers that don't fit the way we want the world to be."
~ Terry Pratchett in Nation