How do chondrichthyes swim?

Animals swim because they have these special structure, and this are the fins and tails, but they cannot swim if they cannot breath under water and this is called gills.

It really depends on the type of animal you are talking about. If you are takling about a shark or fish. Then, see above. If you are talking about an animal such as a hippopotums then they simply do what we humans call a 'Doggie paddle' they use their legs to basically 'Walk' through the water.