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Perek 3 is complicated only on the surface. You may want to draw up some family trees in order to "get" the rather unlikely scenarios the perek proposes, but the underlying concepts are not too difficult, now that we're familiar with the basics from the previous two chapters. (and yeah, I'm also not sure why the Sages find these brain teasers so very interesting but they apparently do!)
The first 4 Mishnayot introduce the category of "the sister of his potential wife", with "his" referring to the surviving brother. When two brothers who had married two sisters both die childless their surviving brother cannot perform "yibbum" with either of the widows, as each one is suddenly now "the sister of his potential wife". The same will hold true if the two deceased brothers had married a different related pair of women, such as a mother and her daughter, in which case each of the women is either the mother of, or daughter of his potential wife. In all these cases "chalitzah" must be performed rather than "yibbum".
Mishnayot 5 and 6 introduce the concept of "ma'amar" (מאמר). Here's the background for what this is: By Torah law "yibbum" is legally achieved through the actual (physical) commencement of marital life (euphamism intended). The Sages however, due to their general aversion to creating the state of marriage through a sexual act, require the "yibbum" brother to first betroth the widow with something of monetary value as we do at a standard chuppah. This betrothal in the context of "yibbum" is known as "ma'amar". The question raised by these Mishnayot is as to what happens if the surviving brother only got as far as the "ma'amar" step before his other brother also died childless, leaving him (as in the earlier Mishnayot) with two widows who are sisters. Beit Hillel and Beit Shammai disagree as to whether the "ma'amar", in the end, is treated as the legal equivalent as actual, Torah-law "yibbum".
Mishnayot 7 and 9, each in their own way make the point that if the surviving brother and the widow were at any point forbidden to one another and thus disqualified from doing "yibbum", they will always remain forbidden to one another even if circumstances change. Mishna 7 presents a case in which the first time the "yibbum" scenario had come up, the widow had been the surviving brother's sister-in-law (i.e. the sister of his wife), but by the second time it came up she no longer was, as her sister was no longer alive (or had been divorced). The second half of Mishna 9 presents a simpler case, in which a couple is disqualified from doing "yibbum" because she is his sister -in-law (as above), but then another opportunity theoretically presents itself when the still-married sister dies. In both cases, since the "yibbum" was forbidden at first pass, it remains so even when circumstances change the impediment passes.
Mishna 8, by the way, takes us all the way back to the cases listed in Perek 1, Mishna 1, and simply injects the new variable of "doubt", i.e. a case in which the marriage between the deceased brother and his "forbidden widow" was to begin with in a state of legal doubt to begin with.
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