It seems the only way to be able to swim with dolphins is to try and do it at the Aqualand water park in Adeje. It's by no means certain that you'll be chosen, out of the various people who might want to do it, but I've found two websites detailing the method you should use to maximise your chances.
If you're in Los Cristianos, you'll need to get yourselves to the water park, but, fortunately, it runs free buses calling at various points in Los Cristianos and Las Americas. For a timetable and list of stops of this free bus, see here.
Good luck with your venture!
PS It would be really nice, if you're going to purchase your Aqualand tickets online, you could use the link on my site! Here's the page: