This repeatable quest can be triggered by speaking to Scribe Neriah aboard the Prydwen, who you'll find on the ship's upper deck. The only prerequisite is that you need to complete the Tour of Duty quest.
Her request is simple: She'd like blood samples of the beasts and creatures you kill in The Commonwealth. When you take down a random enemy, a blood sample will now appear in the corpse's list of loot. There's no set strategy for increasing the chances of finding someone who'll have a blood sample. Our advice to simply kill everyone trying to kill you during your more important quests. The first blood sample we came across was from a Ghoul in a hospital.