For example here http://warpech.github.com/jquery-handsontable/demo/handsontable.html
Is available some tutorial (example) how the entered data record to mysql?
This library already provide an example of save.php script: https://github.com/warpech/jquery-handsontable/blob/master/demo/php/save.php
So you only need to edit this for your own purposes - changing SqLite to MySQL in PDO driver.
And for client-side script you can look at: http://handsontable.com/demo/ajax.html There you have an example how to send data into PHP server.