Guessing it's a prop here :) If so you need to parent the prop to the right body part. Select the prop and double click on it. Select Properties. Click the button that says "set parent" select the body part you want to "glue" the prop to. Say for example the fin is the lower left arm, you'd select Left Foream. OK it a couple of times. Now when you move the figure (without touching the prop) the prop will move along with the figure. Another way is select the prop, and without clicking on anything else in the scene window, in the "Object" menu select Properties. If the fin is a figure you'll need to conform it.

Pinky - you left the lens cap of your mind on again.