The Dead Sea is, besides being the lowest point on earth, a very salty place. It is neither pleasant nor relaxing to swim in due to the high level of salt. It is just very weird and sticky. The main place for a dip is the public Amman Beach which has freshwater showers (you will crave one after a swim), but also a hefty entrance fee. If you want it free, you can drive further south. Expect litter and dodgy looks from local men, but if you are willing to dodge some fence you can cross the road and get access to a hot spring with fresh water.