Do some internet searching and you'll find lots of good info on the subject. It's a pain in the ass and usually stressful.
I'll add one tip though that I think helped, maybe saved us last year (United). First of all, you'll likely need to call it something other than a kayak (i.e. waveski) and wrap it up carefully to pass it off as such. Secondly, whatever airline you use, you should read their policy very carefully, print it out and bring it with you, and know the dimensions and weight limits for what you've decided to call your kayak on the given type of airplane you're flying.
Lastly, my main suggestion, is we had someone call prior to departure and have a note attached to our reservations that said we're bringing waveskis with such and such dimensions and that it's permitted under airline regulations. We were getting some blow back when we first arrived at the counter, but once our reservations were pulled up with the attached note, everything went smoothly. I think a lot of the time the person at the counter simply doesn't want to be responsible for the thing and the note transfers responsibility to someone else. Good luck.