I buy a piece of equipment, walk me through the impact on the 3 financial statements.

A: Initially, there is no impact (income statement); cash goes down, while PP&E goes up (balance sheet), and the purchase of PP&E is a cash outflow (cash flow statement)

Over the life of the asset: depreciation reduces net income (income statement); PP&E goes down by depreciation, while retained earnings go down (balance sheet); and depreciation is added back (because it is a non-cash expense that reduced net income) in the cash from operations section (cash flow statement).