My hometown is right on the Texas Gulf coast, so I've cooked a ton of shrimp. The video MsMoffit posted above is perfect. BTW, always buy wild caught in USA shrimp, shells on. The cheap shrimp is usually farmed in some third-world country with no regulations.
You want shell on, because the shell protects the meat when frozen. Without the shell, freezing can make the meat a little mushy. BTW, any shrimp you buy in a grocery store is, or has been frozen. Even the "fresh" shrimp in the seafood case arrived at the store frozen. So, buy it frozen, and thaw it out yourself for the best freshness.
Thanks for the info on the frozen shrimp. I have never cooked shrimp and DH doesn't like it and actually starts to feel ill from it. I can get frozen shrimp that is harvested in the waters off British Columbia, so decent standards. Also, the fisherman's coop that supplies them makes sure to only harvest sustainably. I might get some when I have more space in my freezer and just thaw a few at a time for me. That video did make it look easy to shell and de-vein them.