Modeling the fins, by Giulio Porta, all rights reserved.

We'll begin with the dorsal fins first, but in your case you can start anywhere your fish has fins, the process, in essence, is the same.
We'll select some edges on the existing portion of the fish, and Extrude them, using the Extrusion tool There are two ways fins can be extruded, we can extrude a single series of edges to make up the fins or double series of edges. In the first case the fins will not have a measurable thickness, they could be referred to as "paper thin", using a figure of speech. Extruding doubles edges instead will give the fins a thickness. We are going with the second manner of creating fins, that of extruding double edges.

 

To select a single series of edges select one first, making sure that both points at the ends of the edge are selected, hold down the shift key and select more edges. In in the illustration here to your right I have selected 3. In you case you may need 4, or more. It all depends on how many cross sections the fish is made out of in that particular area.

Click on the Extrude mode tool. As you can see the fin will not have a thickness. If you need that you'll have to extrude two rows of edges, as well as close its top edge.

To shape the fin ad another spline along its middle from front to back

To finalize the shape of the fin, work in the side view with the rotoscope on, make sure that the splines of edges fit inside the rotoscope. this will be an important issue later because we are going to use the same photo that we are using now as a rotoscope, to texture the fish.
Repeat the same operation for the rest for the fins.

Creating fins with volume or thickness. Some fish, like sharks for example have fins of a sizable thickness. In order to achieve that goal two rows of splines or edges must be extrude to achieve a fin with a sizable and visible thickness. But if you are happy with a paper thin fin, you can stop right now, it depend on what kind of model you want to build, something complex with a lot of details showcasing your modeling abilities or something that will be animated and rendered from a distance where details will not be visible therefore inconsequential.

With the rotoscope turned on drag around the area from which the fins will be extruded, and hide everything else.

Turn the model so you can look down at it. Ad 2 splines, each to the right and left of the existing center spline of the fish. Then detach and delete the original center spline. If that cause some damage to the geometry because of your lack of experience, the damaged patch can be repatched.

To delete a spline is best to detach it first: select the end you want to detach and click on the Detach Point tool

Once a spline is detached it must be dragged away from the point it was detached from, and that point can be deleted if it is no longer needed.

Also once a splined has been detached and dragged away so it "dangles" it can be deleted with the delete key on your keyboard.

When the area that will make up the base of the fin has been defined select all its points with a marquee, the rectangular marquee should do in this case.

Click on the Extrude Mode tool

 

The selected area will be pushed out or a fixed amount, but you'll be able to drag the extrusion higher manually by placing the cursor inside the bounding box defining the extrusion.

Notice that the newly extruded lines are curved inward giving the fin an odd flaring, not suitable for a fin. It would be best if the sides of the fine were straight not curved. That can be easily fixed by Peaking a portion of a curve, you must think about a curve has having two ends, the entire object can be peaked

  Select the portion of the spline that you want to peak and click on the Peak icon. Peaked spines can be curved again by clicking on the Smooth icon.

 

Aside from peaking the splines making up the fin, the fin itself must be closed at the top, keep in mind the extrusion creates a hollow tube and if the end of the tube, in our case the fin, must be closed.

Also unnecessary splines can be detached and deleted.

The preferred configuration of a patch is 4 sided, four side defined by 4 points, a five point patch will not render, in other words it will leave the surface that defines open.

Five point patches.

Five point patches don't render, that means they don't show as a solid surface, that is because the geometry that patches, and their cousins the NURBS, were designed to behave that way, but A:M offers a way around it: the creation of a 5 points patch.

To do so select the 5 point that will make your patch and click on the 5 point icon.

Make 5 point patches only if you absolutely have to.
To continue in refining the fin, you may want to ad another row of splines in the middle of it.
Switch to different view to model more effectively, to admire your work and to avoid overlapping that may result in making the wrong selections.
Another way to define the functionality and the role of a 5 point patch is to think as an area where a spline will dead end because is no longer needed to continue the object geometry.
 
If you fail to make a 5 point patch it could be because you are selecting a spline's end outside the patch you want to close. Don't give up try again in a different sequence, click on points twice if you have to, until the software gets the message.

Repeat the operation for the other fins.