You want a Fisher-Yates shuffle. It is also found as part of the List::Util module. I'm sure if you Super Search the Monastery you'll find it spelled out here too.

For the highest degree of randomness, you just shuffle the list once. This shuffle isn't like shuffling a deck of cards, where you have to do it three or more times to get randomness. The only time you would shuffle more than once is if you have already used the shuffled list, and now need a newly randomized list.