For purposes of the homework, you can just focus on sections 1, 5, 6, and 7.
Chisholm is rejecting Hard Determinism and arguing for Libertarianism. See the last post for what Hard Determinists think and also for a glossary (at the bottom).
Chisholm argues that our choices are not determined, but also not indeterministic. They aren't caused by past events over which we have no control. They also don't occur randomly. He's offering us a third possibility. The third possibility is that when an agent decides to do something, that initial decision is not like the subsequent chain of events. He illustrates with the example of a man grabbing a staff and hitting a stone.
Decision: Man decides to move his handChisholm is claiming that the decision is not an event at all. So it causes Event 1, but it doesn't have a cause. Thus, it's not determined but also not indeterministic. To describe the way the decision causes Event 1, Chisholm uses the term "immanent causation." To describe the way Event1 causes Event 2, and Event 2 causes Event 3, he uses the term "transeunt causation."
Event 1: Hand grasps staff (= stick or cane)
Event 2: Staff moves
Event 3: Stone moves
The homework (TYU3 on p. 604) asks you to "pick an ordinary free action and tell its story in Chisholm's way." So use the model above, but pick something more interesting. You might like to pick one of the (seemingly) free actions in The Manchurian Candidate.
First, read the relevant sections of the article--again, those are 1, 5, 6, and 7. If they sound like gibberish to you, you should still be able to do the homework, using the explanation above.