Metro tickets are requested at any metro station in the Capital Wasteland that still has active protectrons. Having a ticket can prevent one of these robots from becoming hostile. These protectrons are inactive by default, but can be activated if the player can hack a nearby terminal as they then come out of their capsule and search the area for hostiles and passengers. When you activate a Protectron, it will come up to you and scan for a ticket. If it finds one on you, it will take the ticket and leave you alone. Therefore, it is advised that you collect as many tickets as possible if you plan to activate the Protectrons to help you clear the metro. However, as the Protectrons are slow walkers, it is possible to simply avoid one if you don't have a ticket by walking away before it gets a chance to scan for one, avoiding combat.
Metro tickets aren't found in abundance around the wasteland except in Metro stations, but with the add-on Broken Steel, as many as 50 tickets can be found scattered throughout the Olney Powerworks. In one section of the Powerworks, there is a desk with a stack of Metro tickets that are assembled in a traditional triangular card stack.
Some feral ghouls in the Metro tunnels carry tickets, implying that they were passengers before radiation transformed them into ghouls.
xbox360 When the protectron scans the player for a ticket, it will not detect the ticket(s) in the player's inventory and will become hostile. [verified]