SPOILERS:
Gaiman is a genius, today i just read Volume IX, and figured out the whole interconnection with all the previous volumes and Dream's grand suicide. Damn that author is a genius. It does not actually tell you how Dream staged his suicide, but if you connect :
How he felt afterwards, when he was imprisoned by Burgess.
The way Morningstar felt leading to him abandoning Hell.
The way Destruction felt leading to events causing him to abandon his responsibilities and his realm.
All these events had influenced Dream into his grand suicide, and even further influenced by Desire. Dream had interconnected all these events to the right moment.
Desire wanted him to spill family blood, so s/he raped Unity Kinkaid and passed the vortex down to her daughter, then Rose Walker. Desire knew that Dream's authority to kill a mortal if he or she had a vortex. Instead, Desire's plan failed when Unity Kinkaid took back the vortex back into her being. But what was unexpected is that Dream killed his son, Orpheus.
The grand suicide was triggered when Destiny had the family meeting in his realm, with Dream already "broken" because of his eighty year imprisonment, the first influence he would get was from Lucifer, then Destruction, then his grand plan.
At the end of Volume IV, Dream revealed that Loki switched places with Susano-o-no-Mikoto, and Lokie begged that he mustn't go back to his punishment below the earth. So, Dream did what he could, deceived Odin All-Father (temporarily) and Loki agreed that he is in debt of Dream. Now, it did not show what his boon was to Dream any time in the series after Volume IV. But it is safe to assume that part of Dream's grand plan was to enfuriate Hippolyta Hall, thus he told Loki to kidnap Daniel.
Hippolyta Hall swore she would kill the person who ever harms Daniel, so Loki and Puck disguised as cops and gave a false picture of a burned Daniel to Lyta. She furtherly assumed that it was Dream whohad done this. She went to the Kindly Ones for vengeance, but the Kindly Ones said that the revenge only by the chance that person spilled family blood. In Volume VII, Delirium wanted to look for Destruction, and later on Destiny tells Dream that he must consult Orpheus, for he only knows the present whereabouts of Destruction. In order to get this information, Dream owed Orpheus a debt, and that is the long awaited death Orpheus has dreamed of.
So, when Lyta Hall consulted the Kindly Ones, that was the time the Kindly Ones could fuel on vengeance to accomplish their task, for no one wanted vengeance for Orpheus' death. Lyta, assuming Dream killed her son, was told that Dream killed his son and this was the perfect chance for Lyta to kill Dream. Once Dream knew that this moment has come, he made the proper arrangements, had the Corinthian and Matthew seek out the person who kidnapped Daniel and bring him back to the Dreaming. Dream gave Daniel the Eagle-stone emerald, and later on Matthew brought pack the pouch of sand and Dream's helm back to the castle.
Dream finally accomplished his task, he committed suicide by the use of his sister Death, who was one of the few people who knew what his grand plan was. When this happened, Daniel took the proper place Morpheus has given him. Dream couldn't have simply left his realm like Destruction because he knew that there were responsibilities left. He knew that when Dream was away from his realm for a long period of time, the Dreaming slowly fell apart, and he did not want this to happen. So thus he appointed Daniel as the new Dream.
I guess Dream isnt as dumb as Thesaly assumed.