Note that this is only my personal guess of what will happen in A Memory of Light. Nothing here should be taken as a fact or solid information of what actually will happen. This won't fulfill all of the prophesies or expectations of the book. However, this will fulfill many of the large unknown prophesies, such as "He shall hold a blade of light in his hands, and the three shall be one."
First, Rand will discuss his plans with Egwene and the rest of the armies engulfing the Field of Merrilor, and eventually convinces them all that it is necessary to break the seals. Next, Moiraine will Travel to the Field of Merrilor. She will meet with Rand, talk for a short time, then Rand will choose her for the second person to be linked with him in the Last Battle. At the same time, Mat will find out about the Shadowspawn attacking Caemlyn and acts quickly to attempt to defend Caemlyn. He will attempt to meet up with any Kin remaining in the Caemlyn Palace to get them to send a message to Elayne (and anyone else in the Field of Merrilor).
Elayne will receive the message, and Rand will send out a contingent of soldiers/Asha'man (in addition to whatever Elayne sends), but neither will physically go to Caemlyn. Mat will take charge of the defense, and will be too preoccupied defending Caemlyn to be involved with the assault on the Blight. However, the battle surrounding Caemlyn will eventually become as big as the battle in the Blight. The reason the Shadow will focus so much effort on Caemlyn is because Andor is militarily the strongest nation in the Westlands. It has the backing of the White Tower, the Dragon Reborn, is politically interwoven with Cairhien, is fortified with Dragons, and contains the Black Tower itself. Additionally, the Shadow is cocky that they will win already and wishes to strike fear into the hearts of people walking in the Light Capturing their strongest city will do just that.
At the same time, a Civil War will break out within the Black Tower, with the Darkfriends against the followers of the Light. Perrin in Towers of Midnight stated that he would investigate if there was a Dreamspike in the Black Tower next time he slept. Perrin will do so and remove the Dreamspike, inform Rand about its presence, and implore him to send some Asha'man to investigate. Rand will send some reinforcements when he learns of the battle. He, however, will force himself to remain because he must. Perrin's army will be among the reinforcements and Perrin will be in charge of the Light's side of the battle.
With such little men left, Rand very reluctantly informs Nynaeve that he might not have enough men to save Lan in Tarwin's Gap. He will still send most of the rest of his army, but it probably will not hold against the millions of Trollocs. Nynaeve responds that she might decide stay with Lan until the end. Rand understands, but will need a replacement. He thinks upon it, but is unable to come up with a decision that day.
Aviendha returns later that day and informs Rand of what she saw in the Glass columns. Rand decides to force the Aiel Way to return to the Way of the Leaf, AKA the Covenant. Rand then makes the actions to do so. This completely shatters any hope Nynaeve had of Lan surviving. With that, she makes her decision to stay with Lan until the end. She informs Rand, who becomes anxious. Rand decides to meditate on what his decision for a replacement will be the next day while he sleeps.
The next day, Rand has his decision: he will take Alivia. Not only is she very strong (to balance out for Moraine's new weakness in the One Power), she is also 400 years old and very skilled in offensive weaves. She will also help him die, which he knows must happen at Shayol Ghul so she seems the obvious choice. He discovers that Nynaeve has already left to be with Lan in his final moments. He sends the rest of his military to aid Lan however they can. He, Moraine, and Alivia prepare and Travel to Shayol Ghul, with them linked to buffer Callandor.
At Shayol Ghul, Moridin is waiting, surprisingly, with a Callandor of his own! (See  He is linked with Cyndane and Graendal/Moghedien to buffer the effects. Callandor's other "use" (that Min was tasked to find) is that it can act as a sa'angreal for the True Power. A battle ensues between the two groups with neither side victorious. The flaw eventually becomes apparent. The two Callandors link the holders in a way even stronger than the twin balefires. This rapidly increases their connection and the fabled "body swap" happens. Rand, right before he will lose control, tells Alivia and Moraine to kill him, and quick. Fortunately, both understand and are quick to act. Moridin understands that a body swap is imminent. He tells the same to Cydnane and Graendal/Moghedien, but they fear it is a trap. Rand is "killed", his blood is shed, but he lives on in Moridin's body. With Rand in control, he uses his position to force his linked partners to help him re-seal the Dark One. He quickly explains to his previous partners, and adds them to the circle. He uses all three of the Powers (the Saidar, Saidin, and the True Power) to create the new seals. "And the three shall become the One."
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Like I said before this doesn't cover EVERYTHING and what everyone's roles are (ie. Demandred) in the Last Battle, but I have a feeling this is how many of the story paths will lead. Mainly, I believe I am one of the few people that believe Mat/Perrin won't be in the Blight for the final battle.