| Difficult to give you an examples because a cash flow can be very large, and because it just depends on what information you have.
What I can do is give you the rules for the indirect method for the operating section. When they refer to direct and indirect, they are only referring to the operating section, as the investing and financing are always direct. (Whether they say so or not.)
You start with the net income off the income statement and make the following adjustments to it:
1) Depreciation and amortization: ADD
2) Gains, SUBTRACT, losses ADD
3) Current Assets: SUBTRACT increases in balance, ADD decreases in balance
4) Current Liabilities: ADD increases in balance, SUBTRACT decreases in balance
To make that a bit easier to memorize... The first two sets are income statement accounts. You're trying to get rid of them. If it was an expense/loss, it would have been a negative on the income statement. So to get rid of it, you'd have to do the opposite: add. Gains are positive on the income statement, so again to get rid of it, do the opposite: subtract. i.e. these are always doing the opposite of what they did on the income statement.
The third and fourth set are balance sheet accounts. The current assets go the opposite direction as the balance did. If it went up, you go down.
Notice that so far everything has been an "opposite." With the one exception of current lliabilities. They go the same direction as the balance change did. If it went up, you go up also. So I memorize this as being the exception.
Notes: One, do not include cash in the current assets, because the entire statement is cash flow and will take care of cash itself. Two, do not include dividends payable in the current liabilities, because it's actually a financing activity, being related to stock, so it doesn't belong in operating. But otherwise this should work. | 
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