I want to import table rates automatically. What should I do?

First, you need to call this:

Mage::getModel('amtable/rate')->deleteBy($methodId);

OR

Amasty_Table_Model_Rate::deleteBy($methodId)

This will erase any data in the method.

And that is how you make import:

Mage::getModel('amtable/rate')->import($methodId, $fileName)

OR

Amasty_Table_Model_Rate::import($methodId, $fileName)

$methodId is Id of the method in Table Rates, and $fileName is the name of the csv file.