You can read the Anabasis in Brownson's translation at the Perseus Project and in Dakyns's translation at Project Gutenberg.
Book I
It all begins with a succession dispute for the Persian throne. After the death of Darius, the elder brother, Artaxerxes, becomes king; and due to an accusation by Tissaphernes, the younger brother, Cyrus, is accused of plotting to assassinate the elder. Through the intervention of their mother, he is saved from execution and simply banished to the provinces, but Cyrus, having once been entirely in the power of his brother, determined to make sure it could never happen again. He had friends at court, and he set out to build an army of Greek mercenaries. However, he did so in a clever way that made Artaxerxes think he was in fact squabbling against Tissaphernes; he continued to pay tribute to the king. Through connections among the Greeks he built up a sizable army. When he began his anabasis, he continued under this kind of cover for as long as he could -- fighting local enemies. But Tissaphernes was not a fool, and recognized that Cyrus's preparations were far too great to have no other aim than driving away local tribes; he warned Artaxerxes, and the war was on.
Cyrus marched inward, but as he did so, the soldiers increasingly began to be suspicious about what he was doing, and finally, recognizing that he was really marching against the king, they began to resist. One of his commanders, Clearchus, realizing that he was in danger of losing control of his troops, assured them he had no intention of going any further. But Clearchus was playing a savvy game, and used the occasion to make clear to the soldiers just how dangerous and difficult it would be to stop and go back home right then, and that, while the should head back to Greece, they should consider the best way to do so; at their behest, he sent questions to Cyrus, and Cyrus assured the soldiers that he was only marching against his enemy Abrocomas, to punish him; and if he had already fled, the army would then be at liberty to deliberate about what to do next. He also increased their pay. So they continued on, although Xenophon is fairly clear that they still generally thought he was trying to march against the Great King. Xenias and Pasion, two of the commanders, left, probably because their troops were effectively under the control of Clearchus now; because Cyrus knows where their wives and children are, he could have been severe, but instead councils leniency because of their previous excellent service -- which turns out to be the clever thing to do, because it increases Cyrus's favorability among the other Greeks.
Eventually, however, the truth has to come out, and when it does as they are camped by the Euphrates, the Greeks are obviously not happy, and complain that their generals must have been lying to them the entire time. But through some negotiation and the promise of considerable sums of money, most are convinced to continue on. In the meantime, however, one of the generals -- a Thessalian named Menon, or Meno, the very same one from the Platonic dialogue named after him -- had seized the initiative, and convinced his troops to cross the river already to get in Cyrus's good graces. And it certainly does succeed. The armies of Meno and Clearchus, however, will soon come almost to blows, and only Cyrus by skillful management will prevent the disaster -- a noteworthy foreshadowing of difficulties to come. One of Cyrus's Persian allies, Orontas, also betrayed him and was put to death.
All of these problems did not bode well for the ultimate end. The armies of Cyrus and Artaxerxes would eventually meet, at the Battle of Cunaxa. In the battle, the Greeks gave Cyrus a decided advantage, but Cyrus himself was killed. And thus we have the set up of the problem. Deep within hostile territory is an army of well over ten thousand Greeks and no obvious way to get home. But the Greeks themselves did not yet know this; as far as they knew, they had won the battle.
Book II
The Greeks did not learn of Cyrus's death until the next morning; they were puzzling over why Cyrus was late in meeting them when the news came. Artaxerxes demanded that they surrender, but the Greeks replied that it was not custom for victors to surrender to the people they defeated. Miltocythes the Thracian deserted to the Great King, but the rest of the Greek commanders joined forces under the de facto leadership of Clearchus. They began to try to return home, but Tissaphernes came to them, saying that he had tried to suggest the King of the possibility of simply allowing them to leave, but the King wanted to know first why they had come against him in the first place. So the Greeks under Clearchus told how Cyrus had drawn them in under pretense, and saying that they had no desire to harm the King in any way, but just wanted to go home. After a while Tissaphernes came back, saying that he had convinced the King, albeit with difficulty, and that the Persians would gladly lead the Greeks back home, and even provide a market to go with them, in exchange for a promise not to pillage. This was all arranged, although it had to be handled very carefully, since the Greeks and Tissaphernes's Persians were liable to come to blows if ever they came too close to each other.
At the Tigris River we get Xenophon's first mention of himself (2.4.15-17), in company with his friend Proxenus, one of the Greek commanders:
After the evening meal Proxenus and Xenophon chanced to be walking in front of the place where the arms were stacked, when a man came up and asked the outposts where he could see Proxenus or Clearchus—he did not ask for Menon, despite the fact that he came from Ariaeus, Menon's friend. And when Proxenus said “I am the one you are looking for,” the man made this statement: “I was sent here by Ariaeus and Artaozus, who were faithful to Cyrus and are friendly to you; they bid you be on your guard lest the barbarians attack you during the night, for there is a large army in the neighbouring park. They also bid you send a guard to the bridge over the Tigris river, because Tissaphernes intends to destroy it during the night, if he can, so that you may not cross, but may be cut off between the river and the canal.”
Clearchus was agitated when told, but a "young man" -- likely Xenophon himself -- noted that there was an inconsistency between these two purported plans; destroying the bridge would be a foolish thing for the Persians to do, no matter what they planned or expected. Further inquiry uncovered that it was, indeed, a ruse by the barbarian army. But the situation showed a problem -- increasing suspicion among the Greeks that the Persians were really just waiting for the right moment to destroy them. So Clearchus met with Tissaphernes to air their concerns and possibly negotiate some way to allay them. Tissaphernes received him pleasantly, and they mutually agreed that they would share information about anyone trying to stir up suspicion against each other; Clearchus agreed to this in part because he suspected that Meno was one of the ones stirring up trouble in order to seize control of the Greek army. Tissaphernes invited the Greek commanders to a great feast in order to seal the agreement, and five generals and twenty captains went to the feast, with about 200 soldiers along who were going to buy provisions at the market. And Tissaphernes seized the five generals, killed the captains, and had his men slaughter all of the soldiers they could find.
The five generals were taken to the king and executed. Clearchus was one of them, as was Xenophon's friend Proxenus; he gives us a laudatory summation of their lives. He does the same for two others. Meno was also one of them, and it is not laudatory at all -- Xenophon despised Meno, and there is no one in his entire works whom he criticizes so furiously.
So now the Greeks are not only in enemy territory, many of their leaders have been killed by treachery. The dangers of chaos and rout are worse than they have ever been before.
And into this void of leadership will step a young man named Xenophon. But that takes us into Book III.
Additional Comments
* The distances in the Anabasis are often given in parasangs. According to Herodotus, an army could march about five parasangs a day (Histories V.53); this is confirmed by the fact that Xenophon (2.2.6, although this is sometimes regarded as a later interpolation) gives the same Greek approximation as Herodotus, 30 stadia. It was probably not an exact length, but a rough unit based on travel, and it is certainly so in Xenophon -- how long in real terms his parasang estimates are depends on things like weather and terrain (as noted in Tim Rood (2010), "Xenophon's Parasangs", Journal of Hellenic Studies, 130: 51–66).
* It's worth noting the occasional mentions of the market (agora). Greek soldiers were not given provisions; they were paid and then had to buy what they needed from a traveling market -- one of the standard duties of a commander, in fact, was to guarantee that such a market was available.
* We get very little actual view of Cyrus the Younger, but Xenophon's eulogistic descriptions after his death are of a kind he usually reserves only for the very greatest leaders, like the older Cyrus in Cyropaedia or Agesilaus.
* Proxenus of Boeotia was a student of Gorgias; it was he who invited Xenophon to join Cyrus's Ten Thousand. Xenophon depicts him as ambitious but holding himself to high standards of integrity. He was thirty years old at his death.
