Make sure your swimming skills are up to the requisite standard. Take a few lessons if you have not been in the water for a while, or if you are unsure of your swimming abilities.
Book to swim with Belugas at Seaworld (see Resources). While you will not see Beluga whales in their natural environment, this is a good option for those concerned about their swimming ability. The tour takes place in a large pool, and you are able to exit and rest any time you choose.
Swim with Beluga whales in the Hudson river. For the more adventurous, it is possible to go snorkeling with wild Beluga whales as they migrate up the river during the months of July and August.