If a company incurs $10 (pretax) of depreciation expense, how does that affect the three financial statements?

The most common version of this type of question.  Note that the amount of depreciation may be a number other than $10.  To answer this question, take the three statements one at a time.

First, the income statement:  depreciation is an expense so operating income (EBIT) declines by $10.  Assuming a tax rate of 40%, net income declines by $6.  Second, the cash flow statement:  net income decreased $6 and depreciation increased $10 so cash flow from operations increased $4.  Finally, the balance sheet:  cumulative depreciation increases $10 so Net PP&E decreases $10.  We know from the cash flow statement that cash increased $4.  The $6 reduction of net income caused retained earnings to decrease by $6.  Note that the balance sheet is now balanced.  Assets decreased $6 (PP&E -10 and Cash +4) and shareholder’s equity decreased $6.

You may get the follow-up question:  If depreciation is non-cash, explain how this transaction caused cash to increase $4.  The answer is that because of the depreciation expense, the company had to pay the government $4 less in taxes so it increased its cash position by $4 from what it would have been without the depreciation expense.