Dr. Tiedemann is dying of cancer. You can promise to find a cure that was allegedly developed at a secret base in Darwin. Talk to Thrasher near the museum in the Citadel to find out about Darwin’s whereabouts and head there. Darwin is in a high radiation area, make sure you at least buy level 2 radius suits before you get there. You can get them, for example, from Melson.
Darwin is infected with an epidemic developed by Dr. Finister (one of the main villains of Wasteland 1). You will have to get through a group of infected mutants. A single mutant isn’t a threat, but their strength is in numbers, so you might get in trouble if you’re low on ammo. Go to the Darwin Underground Center (you can open the door with the Computers skill, for example). There, in a small room, in a white locker, you will find a bottle of medicine, which you now need to take with you to Tideman.
As soon as you enter Darwin’s underground complex, you will immediately become infected and will need to find a way to treat the infection. For details, see the chapter on Darwin.