"Deveining" has nothing to do with veins. To devein a shrimp is to remove the black threadlike intestinal tract that runs along its back.
Deveining is a good idea when working with larger shrimp, because the digestive tract can contain grit. But whether or not to devein smaller shrimp is a matter of preference. Some people think the flavor of a dish is enhanced by leaving it in (or that it's just too much trouble to remove the harmless tract). The perfectionists among us remove it for aesthetic purposes.
We're not perfectionists here, so we rarely devein shrimp. If you're set on doing it, there are a few shrimp deveining devices on the market -- such as OXO's shrimp cleaner -- but you can just as easily make do with a knife. Peel the shrimp first, then run the tip of a sharp knife along the shrimp's back to lift out the delicate black vein, removing any pieces that break off with your fingers.
Recipe: Broiled Thai Shrimp (Cookthink)
Recipe: Spicy Linguini With Shrimp And Mint (Cookthink)