New main objective: Talk to Arngeir
You can now head to High Hrothgar. Once again find Arngeir, who will inform you that all the invited guests are now in the council room. I'd recommend staying here for a moment, as you will witness the arrival of Delphine and Esbern (screen above), demanding permission to participate in the negotiations. You don't have to do anything, as Arngeir will agree.
New main objective: Take your seat
The council room is in the eastern part of the room. After getting there, you should take a minute and familiarize yourself with the guest list:
The Imperial Legion is represented by Legat Rikke, Jarl Elisif the Fair, General Tullius and Jarl Balgruuf, though the last character will appear only if Whiterun is under control of the Imperial Legion.
The Stormcloaks are represented by Jarl Ulfric Stormcloak, Galmar Stone-Fist and Jarl Vignar, though the last character will appear only if Whiterun is under control of the Stormcloaks.
The other characters present in the room are Elenwen (representing the Thalmor, even though she came with the Legion), Esbern, Delphine and Greybeards.
Once you're ready, sit by the table in the marked spot (screen above).
New main objective: Negotiate a truce
Before you begin the negotiations, it would be good to learn a thing or two about them. The most important information is that regardless of how you behave during them, both parties will eventually reach an agreement and you will be able to force the Jarl of Whiterun to set your plan of catching the dragon into motion. The decision you make during the negotiations will however have an effect on the relations and influences of both parties, i.e. the Imperial Legion and Stormcloaks. You won't be able to remain neutral, so in case you weren't interested in the civil war until now, you will now have to decide who to support. Either way, at the end someone will have to lose and someone gain. It's worth to add that if you have already completed some quests connected with the civil war, it might influence the course of the negotiations. Each fraction will act differently, depending on which areas of Skyrim it controls and who wins at the moment.
As the negotiations begin, Ulfric will speak regarding Elenwen, representing the interests of Thalmor. The Stormcloaks leader will want Elenwen removed from the council room and after a sharp discussion you will be asked to speak (screen above). Your decision will be final, so think about it. If you want to improve your relation with the Imperial Legion, let Elenwen stay by the council table. If, on the other hand, you want to please the Stormcloaks, agree with Ulfric's, point of view that a person not representing any of the factions shouldn't participate in the negotiations.
Only afterwards will you move to the proper part of the negotiations and the initiative will be taken by one of the leaders of the hostile factions. If it's General Tullius, he will probably demand giving Riften to the Imperial Legion. If it's Ulfric Stormcloak, he will demand Markart. It of course won't be one-sided, but an exchange. You will have to decide which city the other side should receive in return (screen above).
If you want to reduce the influence (and lower the relations) of the faction that took the initiative and addressed their demands, you have to choose the upper dialogue option. It's equivalent to forcing them to give up one of their strategic cities, including: Whiterun, Markarth, Riften, Solitude and Windhelm.
If you want to increase the influence (and improve the relations) of the faction that took the initiative and addressed their demands, you have to choose the lower dialogue option. It's equivalent to forcing them to give up one of their lesser cities, including: Falkret, Dawnstar, Morthal and Winterhold. The opposing fraction will most possibly object and you will have to choose between keeping your recommendation, change it or placate the leader with persuasion (Speech).
The further part of the negotiations will consist of a rough speech from the leader of the faction that was treated unfair until now, according to him. It will most probably be the faction that you didn't support in your last decisions. Regardless of whether it will be the Imperial Legion or the Stormcloaks, Esbern (screen above) should unexpectedly join the discussion, reminding all the gathered that the faith of the world is at stake here and that case is most important right now.
The last part of the negotiations will include a speech from the faction leader who still feels unsatisfied with the current settlements and will demand accepting his additional demands. Making the decision will of course your duty (screen above) and you can either agree to the additional conditions (upper dialogue option) or reject them (lower dialogue option). In the latter case the faction can come up with different demands and once again you will be able to either agree or disagree.
The negotiations will come to an end, regardless of whether you agreed to the demands of the "harmed" faction or ignored them and therefore worsen your relation even further. Afterwards listen to Arngeir, who will in detail sum up the conditions of the temporary truce (screen above). As it's equivalent with finishing this quest, you can return to The Fallen (skip to the description of Learn Shout to call Odahviing).
Note - If in the beginning part of The Fallen you didn't consult Esbern on how to find Alduin, you will be now accosted by Delphine. The warrior has learnt that Paarthurnax is a dragon and will inform you that in the past he was Alduin's right hand, responsible for unimaginable crimes. Delphine will therefore demand you kill him, or the Blades won't work with you. A new side quest Paarthurnax will appear in your journal and as it's connected with the main plot, you will find its description in the further part of the guide.