This book is a series of remarks related in complex ways so you can't expect connected exposition in linear order. You will sometimes find Wittgenstein describing a series of examples and then commenting on them, but there is no regularity in this and you will almost never find him introducing a topic and then expanding on it. It is always worth asking why he puts a remark at a particular place (since this book is the result of repeatedly rearranging pre-existing remarks), but such questions can be very difficult to answer and you will often have to read on without having the sense of how it all hangs together that you expect to get from an ordinary exposition. Many remarks will contain a sort of dialogue (often marked by dashes), but it won't be easy to count, keep track of, or identify speakers. Try thinking of such a dialogue simply as one Wittgenstein carries on with himself.
The sections in this assignment concern issues relevant to the picture of language and understanding found in Wittgenstein's earlier work, the Tractatus Logico-Philosophicus (of 1918). §§1-38 are addressed to a primitive picture of language which could motivate the more sophisticated view offered in the Tractatus. That work was a response to the analysis you saw in ch. 12 of Russell's Problems, so many of these remarks are relevant to Russell's views also.
Some sub-groupings of the remarks are distinguished below. We won't be able to discuss all of these; our focus will probably be on the first two and the fourth (i.e., on §§1-17 and 26-38). Within them I call your attention to particular remarks but our class discussion need not be limited to these; one way to prepare for discussion of Wittgenstein is to draw up your own list of remarks that seem important or otherwise interesting and also another list of remarks that are puzzling.
§§1-7. Augustine's picture. Concentrate on the picture of language presented in the quote from Augustine, contrasting it with the uses of language described in the shopping example later in §1 and comparing it with the builders' language of §2. The idea of language games introduced in §7 is important--think about why this term is used and what purpose is served by the discussion of language games. (The ideas of ostensive definition and ostensive teaching introduced in §6 will be referred to later.)
§§8-17. Varieties of words. Notice the variety of words in the extension of the builders' language in §8, consider the difficulties of applying a single concept of signification to all of them, and notice the analogous difficulty in §11 and §14. Notice also the "straightforward" application of the idea in §15. This is one example of a frequent contrast between homely applications of concepts and philosophically ambitious ones; another example of such a contrast is the application of the concept of naming to the first builders' language and in Augustine's picture.
§§18-25. Varieties of use. The chief idea in the earlier sections of this group is that language has a variety of uses, all with equal status: a language consisting solely of single-word commands is not incomplete and, when statements appear along with commands, they are not more fundamental. Think about the variety catalogued in §23 and try to extend the list; it is characteristic of Wittgenstein to emphasize the importance of a varied diet of examples. (The idea of a "form of life" mentioned in §19 will reappear in some important places.)
§§26-38. Naming. These remarks contain a compressed example of Wittgenstein's typical analysis of philosophical error. Naming is labeling in preparation for use (§26), so ostensive definition presupposes a wider context of use (§31) which Augustine's child brings with him like an adult foreigner (§32). It may seem that what is required is a psychological act or experience (§33, beginning) but there is no single experience that serves (§35) and the experience as such is not what is essential (§33, end). We invoke the mental where the physical seems insufficient (§36) but that is because we try to find in an act or event what is due to the context of use in which it occurs (§37). Real mental acts or events satisfy us no more than physical ones, so we are led to regard naming as occult (§38).