How can I get a villager without a village?
Creative mode / Commands
If you are using Creative mode, you can simply use the Villager mob egg available in the inventory or type the command /summon Villager ~ ~ ~ (summons villager at your coords).
Curing a Zombie Villager
In survival, the way to get a villager without a village would be to cure a villager zombie. You can tell these apart from regular zombies because they look similar to villagers.
To cure a zombie villager, you will need to trap it so that it can't escape and won't burn during the day, then hit it with a splash potion of weakness and then feed it a golden apple. After a few minutes the zombie should change into a villager. You will need 2 of these in order to breed more.
Once you have two villagers, you need to build a "village" in order to have them breed. There's a very detailed tutorial on the Wiki, so I won't go into detail here. Keep in mind that in 1.8 snapshots and in the future 1.8 update villager breeding requirements will change. Specifically, you will need to trade with them so they become "willing" and then they may randomly breed. It's also possible to get "farmer" villagers to be willing by letting them harvest wheat. This video from docm77 shows an automatic villager breeding setup for 1.8.
Potionless Zombie Curing
If you don't have access to a nether fortress in your world border, you won't be able to make potions because you can't get nether wart or blaze rods. However, you can still heal a zombie villager by trapping a witch with the zombie and standing within 3 blocks till the witch throws a weakness potion, then feed the zombie the golden apple. You can drink milk to remove the potion effects from the witch while you wait for the weakness potion (25% probability when standing within 3 blocks).
If you'd like you can watch a video that shows this exact scenario happening on the new Mindcrack Server. Etho, Sethbling, and Nebris cure two zombie villagers using a witch, because they are using a world border and don't have a nether fortress. Etho's perspective (toward the end of the video), Sethbling's perspective (toward the end of the video), Nebris' perspective (also toward the end).