booz's results aren't typical, though, by just adding a cocktail shrimp. It normally takes a few weeks to a month to fully complete a cycle.
You really don't want to "skip" your cycle, but there are some things you can do to speed it up: buy cured LR, and cured LS from an established tank. These already have the needed bacteria to process ammonia, so when you add your shrip to kick off the cycle, a whole colony doesn't need to grow from scratch (which is what takes so long) but the existing colony just needs to grow more. This is the best way to shorten your cycle without skipping corners.
NOW, the big thing you need to do before doing this is to ask the owner if they've ever treated with ANY medication in that tank. If so, the LR and LS could be contaminated with some sort of chemical, which could cause your tank to crash. So, if you want to take a short cut, make sure it's a safe road and not some dark back alley.