Dr. Klein: by following various dialogue routes and having a good level of the Medicine or Science skill, the Courier can gather info about the other courier, Ulysses, and Father Elijah.
Dr. 8: if the Courier has at least a Perception of 7 or Science skill of 75 they may, through dialogue, understand Dr 8. With the Science skill they can choose to program him to mindlessly do what they want.
Dr. Borous: the Courier can talk to him about the fact that his experiments have escaped the Big MT and into the Mojave, although he refuses to believe the Courier.
Doctor 0: if the Courier passes a Speech check of 65 and Intelligence check of 7, or has the Math Wrathperk, they can work out his real name is "Dr. Zero". With Intelligence of 9+ they can teach him how to differentiate 0 and O with a slash.
Dr. Dala: if the Courier has a high enough Medicine, Charisma, or the Cherchez La Femme/Lady Killer perks, they can work out that she misses her body and secretly has some sort of fetish for teddy bears, which can be used to complete her portion of the quest. Teddy bears can be obtained in Dr. Dala's room on the 2nd floor of her home in Higgs Village.
Talk to Dr. Klein, despite your lack of earmuffs.
Chat with Dr. O.
Introduce yourself to Dr. Dala.
Say hello to Dr. Borous. Carefully.
"Speak" to Dr. 8 - if you can.
There is no set order in which the Courier needs to talk to them.
By picking the right response with each think tank, the Courier can gain extra supplies and caps.
Picking the correct response when talking to Dr. 8 can gain the Courier some good Karma.
By picking the right response with each think tank, the Courier can avoid fighting them later in the main quest.