As always, please read with a gemara in front of you. It will just make more sense that way.
The gemara discusses netilat yadayim, washing one’s hands for ritual purposes, and addresses the case of pouring water on one and immersing the other. At least, this is the way Rashi explains it. Rabbeinu Tam, though, (Tosafot הנוטל), has a different edition, in which the case is very different: A hand is washed from a single pour, instead of the usual multiple pours. Ordinarily we require two pours in order to remove the first water, which has contracted tumah (some do three, for separate reasons), but here we are saying that if the second pour with a double portion of water, that suffices.
The gemara talks about a get held by two deliverers. Rashi seems to say that both must, literally, grip the document, but Tosafot (אבל) disagrees.
I am very troubled by the יתד היא שלא תמוט answer offered by R’ Ami to justify issuing two contradictory legal statements, one stricter and the second more lenient. If R' Ami means that his former, more stringer position, is a decree to prevent trouble, then this decree will end up creating agunot unnecessarily, something the gemara has explicitly said we avoid (such as the bottom of 2b, top of 3a)!
R’ Yochanan and Reish Lakish offer reasons why we require a date on a get document. Rashash notes a third reason: To establish at what time the husband ceases to be “related to” his ex-wife’s family, for the purpose of validating or rejecting his role as a witness in a court case.
The gemara seems to say that extramarital sexual relations are rare and therefore not worthy of rabbinic decrees dealing with its occurrence. This does not seem to be the case, given various rabbinic enactments which are instituted for such cases, such as the preference for Wednesday night weddings in order to expedite a Thursday morning trip to court (Ketuvot 2a)! Tosafot זנות explains that sexual immorality is, indeed, not considered unusual; what is unusual is such an occurrence with witnesses and a legal warning.
Rav and Shemuel debate how to count the 3-month “havchanah” waiting period for a woman who has been divorced and wishes to re-marry. (The goal of havchanah is to ensure that we can properly identify paternity of a child born severeal months into her second marriage.) Rav says to count from the time the get is delivered, but Shemuel says to count from the time the get is written. The gemara says we follow Shemuel, which is unusual; we usually follow Rav on prohibitions, Shemuel on financial matters! Perhaps, though, we follow Shemuel here because of the latter amoraim who took his side – Rav Ashi, as well as Rav Kahana and Rav Papi.