On this page of the game guide to Borderlands 2 you will find detailed walkthrough descriptions of the side missions titled Claptrap's Secret Stash and Do No Harm. Both of these quests can be started in the Sanctuary location after completing the main mission named Plan B.
You can receive this mission after completing Plan B.
1) Claptrap and Stash
Find Claptrap  and speak to him twice. Once he's done with his monologue, turn around 180 degrees and approach the stash shown in the screenshot. When you get close enough, the steel covering it should fall down. Use the stash and finish the mission be speaking with Claptrap. Using the stash, you can transfer items between all your characters.
1) Zed's clinic
Head to Zed's clinic  and speak to him. Melee attack the patient (by default V) shown in the screenshot and pick up an Eridium Shard which will fall out of him. With it, go to Tannis who can be found at the ground level of Roland's hideout . Speak to her to end the mission.