I've done it both ways. Not paying is easier, but you do pay for the remainder of the month you're in, which you presumably don't want. Calling will get your service stopped that day if you say "CANCEL". If you say "SUSPEND", you will begin paying five bucks or so per month that you don't need to. CANCEL is the way to do it.
Either way, for the next thrity days Dish will pretend you're actually a deliquent customer. If you call them back they will assure you it's OK, but if you restart your service within that 30 day period, you will pay for all the previous days your service was off, as if you had never cancelled. After 30 days, you're fine.