Layout Foot length Jacket Cape
I'm assuming from your question that you're looking to have the cape flared out around and behind you while you are standing still, as the cape will naturally take that shape when you're in motion. My best recommendations to accomplish that appearance would be to use plastic ("boning" for corsets) or wire (strong but flexible, ie. aluminum armature wire) that can be used to shape the cape. These would be run down the sides where the black trim is located, starting at waist height or higher, as well as across the bottom hem.

I will not offer these suggestions without the following warnings, however:


The cape will likely look unnatural both at rest and in motion. You may be able to skillfully shape it to look more natural at rest, but it will still look stiff when you're moving
You will likely become annoyed very quickly while wearing it. If you're planning to wear it to a convention, they are generally crowded, with a lot of narrow passages, and a stiff cape like this may interfere with your moving around. You'll also become annoyed trying to pack or store it because of the stiffness. And on top of those issues, you also won't be able to sit down while wearing it (and likely would become unwelcome in panel spaces due to the size anyway).
If you are wearing it at a convention, you will quickly become other attendee's least favorite person. You will likely have a reduced awareness of where the back of your cape is, and you will hit people's legs, belongings, and props, as well as potentially knocking over displays in vendor areas, and taking up a lot of space in crowded areas.
If you are wearing it at a convention, you may be in violation of costume policies for that convention. Many will have rules such as the "Six Inch Rule," where no part of your costume may protrude more than 6" from your body, and the shaped cape would easily fall outside that limit. You may be asked to remove the piece from your costume or leave certain areas if convention staff determines you to be in violation of rules or a hazard to other attendees.


In light of those problems, I would recommend you do not focus on making a stiff cape. Rather, you should evaluate fabrics that will move and drape in the proper manner, to get the right look in motion, and to make the entire costume much simpler to wear.

I will also take a brief moment to address the solutions offered by abbie, which won't work as well as expected. Fabric stiffeners are meant for very lightweight fabrics; unless you're making the cape out of chiffon or cheesecloth, you aren't going to get any noticeable stiffening. I have used various stiffeners on thicker fabrics; they do not harden as you would expect, and form "break points" that fold severely and look quite bad. Starch definitely won't work, as it's meant to keep wrinkles out but keep fabric still wearable. In these cases, you're going to end up with a rigid cape that hangs straight down and doesn't move at all when you move.

Interfacing may work, but only if you use the heaviest form (often sold as "craft interfacing") and line the entire back of the cape with it. I frequently use heavy interfacing in my own costumes, and it is still quite flexible and would not be able to support the weight of the costume at that size. At best, you will likely get a stiff cape hanging rigidly around your legs; at worst, it will partially flare before giving in to your own weight, leaving you looking like you are wearing a bustle, which I assume is not the look you are after. Lighter interfacing will not stiffen the fabric at all.

Crinoline may work, but at the size it would need to be, it will be highly visible, and no more effective than directly wiring or boning the cape itself. Tinfoil will obviously not work, as it's designed to be very pliant, and chicken wire is likely to damage the costume pieces and your body.