1. How to hold the camera.
2. What camera to use.
This doesn't matter as much as the correct lens. If you have a choice though I would personally prefer faster burst rate over megapixels or sensor size (ie. Canon 7D over 5D mkii). Additionally if don't have the endurance to hold the camera for nearly 30 min a heavier full frame camera might cause you to miss the shot.
3. What lens to use.
Telephoto would be better than wide angle for obvious reasons. (ie 70-200, 70-300, 80-400, 100-400). Pay attention to the whales behavior, and look for patterns in their actions. This is where a zoom telephoto lens can help you frame your shot versus a fixed focal length telephoto lens could cause you to miss the shot.
4. What settings to use.
If you normally shoot in the green mode this might not be the time to experiment. However if you are ready for the big leagues it might be time to checkout TV and M. I would personally not be as concerned with my depth of field. Depending on the time of day I would pick a ISO that would guarantee the best noise performance. To paint a broad stroke I may choose 400-800 ISO, so that I can achieve a fast shutter speed to freeze that action. I would pick a shutterspeed that would be double my focal length. (ie. 200mm >> 400 >> 1/400 sec). I would place the drive into burst mode. The AutoFocus would benefit from continuous mode rather than single shot.
5. How about memory card?
Large and Fast. This will depend on resolution of your camera, and if you plan to shoot RAW or JPEG.
6. Don't forget to put the camera down, and enjoy the experience. Who knows when the Mayans plan to end the world next? Please comment below your recommendations or questions.