"Have you ever spent days and days making up flavors of ice cream that no one's ever eaten before? Like chicken and telephone ice cream?...Green mouse ice cream was the worst. I didn't like that at all."
Todd Klein, the series' letterer, draws Delirium's speech as a scrawl against a multi-colored background; sometimes the background color will match the mood she is in (red for anger, blue and green for calm, etc.).
Very occasionally she is able, with an effort, to become more controlled in thought and speech, at which point her speech is drawn more neatly and the background fades to near-white. This effort, as she says later, causes her pain. Her speech as Delight in Endless Nights takes the same form, with somewhat orderly lettering and a faint rainbow background.
As her name suggests, Delirium is scatterbrained and easily distracted; she often forgets the thread of her conversations and comes out with offbeat and seemingly inconsequential observations.
Delirium often has a playful attitude, regarding some events with ecstatic joy, such as being held above the ground by the Wyvern, to Destiny splitting into multiple incarnations before her. Delirium is also quick to respond angrily to rudeness, leading her to occasionally punish people without mercy; usually with a form of madness.
It may be noted that Delirium once exhibited a very deep form of order. Towards the end of Brief Lives, as she recounts to Destruction the steps she and Dream undertook to find him, her appearance - hairstyle, clothing, et cetera - recapitulates in almost the exact order it had originally appeared. Her long and rambling recollection seemed nonsensical, but readers noticed that it more or less accurately described everything that had happened - just not very clearly. This suggests that Delirium may be less mad than she appears and merely has trouble expressing herself. Also, when Destiny imparts to Dream the information and the means by which he may find Destruction; due to Dream's distress at this revelation, Delirium is forced to collect herself so much that her usual mismatched appearance vanishes, and she becomes a very symmetrical creature, reflecting perhaps that in delirium, delight still exists, no matter how painful.
Delirium, like her siblings, has also exhibited a form of prophetic knowledge; however, her prophecies rarely make sense until it is too late to do anything about them, and no other character recognizes them. In Brief Lives, she persuades a man to give the dancer Tiffany money, when Tiffany would later be the only mortal to survive the explosion of the club where she was dancing; in The Kindly Ones, she knows full well that her brother is in trouble and unsuccessfully tries to persuade him to help her find Barnabas. Additionally, when read the quote 'Quoth the Raven', from Edgar Allan Poe's poem, 'The Raven', she says 'Whatever', which had been and would be said by Matthew throughout the book.
Delirium also seems to know many things none of the other Endless know. She says so when she is teased by Desire during the family meeting in Season of Mists. At the end of Brief Lives, Destruction describes a situation in which Death told him that everybody knows everything and they just pretend they don't, but neither he nor Dream really understand or believe this. Delirium, however, says, "She is. um. Right. Kind of. Not knowing everything is all that makes it okay, sometimes."
The other Endless, particularly Death and Destruction, seem to be fond of Delirium, to varying degrees, and protective of her. She in turn is affectionate towards them, particularly Destruction. Initially, she was somewhat frightened by Dream and avoided being around him, to the point that his guardians did not know who she was, however, the events of Brief Lives change their relationship. Delirium desperately tries to help save Dream from his impending doom in The Kindly Ones by trying to persuade him to go with him on another quest with her to find Barnabas, but Dream refuses.