On this page of the game guide to Borderlands 2 you will find a detailed description of the side mission titled Animal Rescue: Medicine. You can begin this quest in the Lynchwood location during the completion of the side mission named The Bane.
3) Tunnel to the northern part of Lynchwood
In the spot marked as  on the map you will find a sleeping Skag Dukino. Approach it and destroy his chain with a melee attack (by default V).
Now you need to obtain the Medicine which can be found on the roof of the building . In order to get there, head onto the roof of the building to the left of the roof with the medicine (stairs can also be found on the left side of the building). Head to the other end, following the ledge on the right wall. You will eventually reach a tank from which you can easily jump to the Medicine. Place the medicine in the designated place, beside Dukino's kennel.
The next stage of curing the animal is collecting five Skags on a Stick which can be found in the northern part of Lynchwood (passage marked as ). After finding all the items, return to Dukino  and throw in the food from the left of the kennel.