This post is targeted for storing multiple animations that can be brought into a gaming engine like Unity. This post is built on top of 2 other previous posts.
To learn how to create a rig go here: Rigging Intro
To learn how to animate a rig, go here: Animate Rig
Building off these two the next step is to store several animations of the same armature in one blend file. To do so, when you are in the Dope Sheet view and capturing your animation, you'll need to set the Mode to Action Editor.
Give the current animation a Name (in my case I called it "swim"). And be sure to click the [F] button, as this creates it as a unique animation in the file.
Click the [+] sign to create a new animation, and give it a new name. You'll need to delete all the previous keyframes (except perhaps the first), then add new animation. Once again, make sure to click the [F] button again so that it is identified as unique animation.
To see how to configure this animation in Unity, go here: Import Animation Model