The Siege of Atlantis was a battle in the Second Olympian War. The Titan Army, which was led by Oceanus, attacked Atlantis, in an effort to overthrow Poseidon. This was part of the Titan plan to split the Gods, to prevent an Olympian victory. The plan ultimately failed when Poseidon, under the urging of Percy Jackson, chose to attack Typhon in New York. From what we know it wasn't really a siege but a battle by Poseidon's Palace.
The Atlanteans were led by Poseidon and his commanders. They seemed to mostly consist of Mermen, Fish, and Cyclopes. Poseidon himself individually destroys the most powerful of the monsters, but does not enter the battle for real until he has to face Oceanus himself in direct combat. Also, Briares, the last Hekatonkheire alive, has joined the battle. It is mentioned that there are armies of dolphins and sharks in reserve in Atlantis, which are unleashed when Percy arrives in Atlantis.
The Titans were lead by Oceanus. Poseidon mentions that Oceanus had brought out old and shockingly powerful monsters that he had nearly forgotten to have existed at all. The forces included mermen, Oceanus himself, leviathan lobsters, giant serpents and monstrously huge squid and eels.
Not much is known about the Siege of Atlantis until The Last Olympian. It can be presumed to have started several months before the beginning of the book, since the battle seems to have severely destroyed Atlantis and massacred millions of its inhabitants - there are a multitude of hastily-made graves throughout the palace. Poseidon mentions in The Battle of the Labyrinth that the fighting has already become almost unendurably intense, even before Oceanus himself duelled Poseidon.
After the Battle of the Princess Andromeda, Percy finds himself in Atlantis. His half-brother, Tyson, is helping in the Armory and was visiting him. Percy is shocked to see Atlantis at war, and talks to Poseidon. Poseidon warns Percy to be careful, and reminds him of the birthday gift he gave him. Poseidon then leaves to fight Oceanus. The Battle is so destructive, especially between two warriors as phenomenally powerful as Oceanus and Poseidon, that it causes riptides, tsunamis and incredibly violent aquatic storms.
At some point in the battle, Tyson was permitted to fight, which later lead to his promotion to General. After Percy talked to Poseidon about attacking Typhon, Poseidon agrees to do so, providing major support in the final battle against the Titan. It can be assumed that the city has been rebuilt since then, but the damage done was still immense.