I need to update/amend my state return (Illinois). How do I just update the form directly?

First explain what you have done so far.  Has your IL return already been e-filed?  

It was e-filed, but I received a notice from the state regarding an error.  I know what the error is, and it would be easier to update the form directly opposed to going through the questionnaire.

You cannot just go on the tax form and "update" it.  The software and the filing process do not work that way.  You will need to amend.

To amend only a state return:

https://ttlc.intuit.com/questions/2824532-i-need-to-amend-my-state-return

 There are instructions in TT to "calculate your contributions manually" on the form...how?