This week's tutorial on how to make a fish swim. Tutorial 2

By far, I found this tutorial to be the most helpful and it seems to produce the most realistic result.

http://cgswot.com/tutorials/vfx-tutorials/116-07-underwater-scene-in-after-effects-part-1.html#disqus_thread

In details, the video talks about the way we can make objects move more or less realistically. In an example of the fish, the first step is to divide a fish on several areas that are going to be moving. So, the head and the body, tail and back fin. Then we create a mask over a fish and set mask settings to none. then we copy the mask and move it to the next area of the fish, by dragging only one side of the mask. This way masks stay together and we do not see any stripes on the fish. After we make all four masks for four areas of the fish, we copy the fish four times, and delete extra masks on each fish, so that each one has different mask on it.
Then we set all of the masks on add, and set the spindle centers on all of the masks on the left edge if the fish is facing left.
The next step is to set up the parenting. The head is the parent of the body, the body is the parent of the tail and the tail is the parent of the back fin. After that we can set up the movement of the fin, tail and body and place a looping expression on the frame.