Propaganda: the Persians
Both sides tried their hand at spin following the indecisive Battle of Artemisium. Xerxes, worried about the loyalty of his allies, invited them to come and see the Greek corpses at Thermopylae (having stage-managed the scene first). Herodotus:
There were about 20,000 Persian dead at Thermopylae. Xerxes left around 1000 where they lay, and buried the rest in trenches, scattering leaves over the top so they wouldn't be seen. Then he sent a herald to assemble the entire naval force [now camped on Euboea]. "Allies," he said, "king Xerxes gives you permission to leave your posts and come and see how he fights fools who hope to overcome the king's power." After this boats were hard to come by - everyone wanted to go sightseeing.Herodotus, Histories 8.24
Propaganda: the Greeks
Xerxes wanted to boost the morale of his Ionian Greek allies; Themistocles decided to try and persuade them to desert. Along the coast of Euboea, wherever the Persian fleet might put in to get water, he had a message carved on the rocks for the Ionians to read:
Ionians, you are wrong to be fighting against Greece, the land of your fathers. Desert and come over to our side - or if you can't, deliberately fight like cowards."Herodotus, Histories 8.22
Herodotus reckons it's win-win for Themistocles. Either the Ionians desert, or Xerxes will think he'd better not rely on them.
The Persians move south: target - Athens.
The Spartans and other Greek allies decided to build a wall across the Isthmus at Corinth to stop the Persians getting into the Peloponnese. Everywhere to the north was abandoned to its fate - including Athens. The Athenians had evacuated their city as soon as the fleet got back. All wives, children and slaves had been packed off to safer places - most of them to the island of Salamis, where the fleet was waiting for the Persians.
Athens was almost empty when the Persians arrived. A few people, though, had built a barricade for themselves on the Acropolis, convinced that this was the "wooden wall" the oracle talked about. Even when the Persians set fire to their barrier using arrows tipped with pitch, they refused to surrender. Finally some enterprising Persians found a route up the "impregnable" rock. A massacre followed. The temple of the goddess Athena was looted and then burned. The fleet shortly afterwards arrived at Phaleron. A messenger was despatched to take the good news to Susa.
According to Ctesias, Xerxes then set his men to work building a causeway across the strait separating Athens from the island of Salamis - a comparable feat to the Bridge of Boats and the Canal through Mount Athos. If Xerxes ever did start it, the project was not completed.
The Battle of Salamis 480 BC
We can't now know what actually happened in this battle - everything is controversial: exactly where they fought, how many ships were involved on each side and even what the strategy and tactics were. Herodotus wrote 40-50 years after the battle and could not have interviewed any of the commanders; he must have relied on stories from old men who'd been rowers in the fleet who had probably been pretty confused themselves about what precisely was going on. As usual, he tells us of a few entertaining incidents, without giving a clear overall picture.
Our other source is an Athenian play (The Persians of Aeschylus, already mentioned) - whose author probably took part in the battle (though not as a rower). The Persians was produced in 472 BC (and won the prize) - only 8 years after the battle: the audience might have noticed if any facts were seriously wrong. But would they have expected historical accuracy from a poet? Especially as most plays were based on stories of the Trojan War or other myths.

Salamis, satellite image showing the straits where the battle was fought on the right (Photo NASA)
See if you can work out what happened from this description and the map. A Persian messenger brings the terrible news to Xerxes' mother Atossa that her son's attack on Greece has been a total disaster.
Your majesty, an evil demon began it. A Greek came over from the Athenian fleet, and had this message for your son, Xerxes. "The Greeks intend to slip away tonight when it is dark, to try and save their skins." When Xerxes heard this, unaware of the Greek trickery, and the malice of the gods, he told his captains: "As soon as it's dark, split the main body of the fleet into three lines, and send the rest round to the other side of Salamis, so you can block off all their exits". The captains, he said, would be beheaded, if any Greeks escaped. He spoke confidently, ignorant of the future the gods had in mind.Obediently our sailors had their supper, sorted out their oars. As the light faded, they climbed aboard, rowers and marines. The lines shouted cheerfully across to each other, and sailed out, just as they'd been ordered. All night the captains kept their crews patrolling the straits. But by dawn, there was no sign of the Greeks attempting to break out. Then, as the sun came up, the Greek battle-cry echoed round the rocky shores. Every barbarian felt sick with fear, knowing we had got it wrong. The Greeks did not sound like deserters; it was the warlike noise of men ready to fight. A trumpet sounded. We could hear the plash of oars as they churned the sea.
Then we saw them. The right wing appeared first, ships in line, rowing in unison. Next the whole fleet came into view, and we heard their shouts: "Come on, you sons of Greece, it's all to fight for: let's free our land, let's free our children, our wives, the temples of our gods, the tombs of our ancestors." From us came a confused reply in in Persian tongues.
There could be no more delay. Ship rammed ship, bronze beaks to the fore. A Greek ship struck first, smashing off the stern of a Phoenician. Then it was a free-for-all. At first the Persian fleet held firm, but as more of our ships crowded into that narrow strait, we could no longer help our friends. Our ships crashed into each other, snapping off their oars. The Greeks, as they planned, encircled us and closed in. You couldn't see the water for capsized ships, wreckage and corpses. Rocks and beaches were draped with dead. All the Persians ships could do was fight to escape the chaos, while the Greeks used oars or bits of wreckage to spear the survivors in the sea, like fishermen killing tuna trapped in their netsAeschylus, The Persians 357ff tr AMW

Killing tuna in the traditional way in the Mediterranean
The Persian plan had most probably been to land on Salamis and finish off Athens by killing the population that had taken refuge there. For this purpose they had stationed an élite task force on one of the small islands in the strait (we're not sure which). The messenger in the play goes on to describe the bloody carnage when the Greeks landed on the island. It's so vivid, that it's thought Aeschylus himself might have been one of those involved in the butchery of the Persian guards.
After the Greek victory at Salamis, the Persian army withdrew to the north of Athens for the winter. Xerxes himself, who'd watched the battle from the hillside opposite, returned to Asia (Sardis) leaving his cousin Mardonius in charge. He'd conquered Thessaly and Boeotia, and captured Athens. Battles won 1, drawn 1 lost 1. What were his thoughts?
Queen Artemisia: a postscript?

The Xerxes vase (British Museum)
A small vase in the British Museum suggests an intriguing postscript. Among the objects found in the tomb of Mausolus of Caria (who ruled 357 to 353 BC) - the original "Mausoleum" - is a 30cm high jar made of calcite, probably from Egypt. It carries a simple inscription "Xerxes the Great King" in four languages: Egyptian, Old Persian, Babylonian and Elamite. This is interesting first of all because it illustrates the multicultural nature of the Persian empire (and perhaps confirms Aeschylus' verse about "confused Persian tongues" - above) - it was seemingly routine to use several scripts.
But what was a jar with Xerxes' name doing in the Mausoleum? The most likely explanation is that Xerxes visited Halicarnassus after his return to Sardis (Herodotus doesn't mention it, though) and gave this little gift of an antique vase to Queen Artemisia (to show his admiration for her?). It then passed down among the treasures of the ruling family until it ended up in the tomb of Mausolus - and his wife, who was also called Artemisia.