Step 1: What You Need
1/2" plywood: this would all fit in one 4x8 easily. I used scraps lying around.
25" of 2x4, or 50" of 2x2 for the inside support.
15" x 15" of foam (I had 3" around and used that, if I were buying it I'd probably go thinner).
2 cheap 14" IKEA pillow forms for additional padding on top.
Fabric for cover (I had two pretty pillow cases that I used for the top, and bought 1 yard matching fabric for the rest, fabric not pictured).
hinges/1/2" screws for hinges.
screws for building the frame (2" or 3" works fine).
Table saw/miter saw (or whatever you have to cut wood)
Orbital sander or sandpaper
Step 2: Sand the Wood
Step 3: Cut the Wood
(x4) 12" of 2x2
(x2) 12" x 15" of 1/2" ply
(x2) 12" x 14" of 1/2" ply
(x2) 15" x 15" of 1/2" ply
Step 4: Assemble the Frame
Next attach the 12"x15" pieces to your two half assembled sides. Be aware of where your other screws are, so they don't hit each other. Now you should have a square frame.
Last, attach one of your 15"x15" to one side of the box for the bottom. The remaining 15"x15" will be upholstered separately and attached at the end.
Step 5: Cut the Foam
Also shown is the buildup for what will be the top of the ottoman.
Step 6: Sew the Upholstery
Cut your loop into two loops, one to attach to the top square, and one for the bottom frame. Leave a few inches on both for wrapping and stapling down later. For me, this meant about 5" for the top and 16" for the bottom.
The next step is to sew the top square to your 5" loop of fabric which will make the sides. In my case I used pillow cases that were slightly larger than 15" square. You could also use more of the same fabric. Regardless, you should have a finished top size of 15"x15" (equal to your frame), and should add a quarter - half inch to that for seam allowance depending on the strength of your fabric. To sew on the top, put face sides together, and pin before you sew all the way around, ESPECIALLY if you are sewing a non-stretchy to a stretchy fabric. Make your seam, and turn right side out.
The last piece of the upholstery is to make a flap for easy opening. I pillow cased, then topstitched, a 1" x 6" strip for this purpose, which will be stapled to the top.
Put your pillow, foam and remaining piece of ply in the top, bottom fabric over the frame, and check out how great it's going to look!
Step 7: Attach Upholstery
Do the same for the bottom frame, although because there is less stretching necessary I just moved in a circle around the top and bottom.
At this point, there are many options for making things prettier. I cut the edges neatly and glued them down, and later decided to glue down a ribbon to clean things up further (hence there being hinges in these later photos). You could also line the inside with fabric or paint it for a fully polished look, but I skipped this step in the interest of time.
Lastly if you plan to use this on bare wood floors, it is important to add felt corners to the bottom so the staples don't do any damage.
Step 8: Add Hinges
Enjoy sitting on your new ottoman, and having a new place to store things!