The shrimp isn't necessary, but is a common way to kickstart a cycle. Basically you want to introduce a source of ammonia to kick off the cycle. If you get live rock, there's usually enough die-off in transit that you'll have the ammonia needed, you can also add some fish food, add a hardy fish (NOT RECOMMENDED) or (I'm not kidding...) pee in the tank.
Since peeing in the tank is just weird, adding a live fish is cruel, and die-off or fish food take a bit longer to convert to ammonia, the shrimp is a more commonly accepted practice.
I've never used a shrimp, and my tank has always naturally cycled in 4-6 weeks.
While some people advise to leave your filter and lights off during the cycle, I tend to run my tank just as I plan to run it with livestock after the cycle. By running lights and my skimmer, I not only get through the ammonia cycle, but I also get through the algae cycle, and ensure that everything is running properly before I add any livestock. The only tank maintenance that I skip during a cycle is water changes.
