Also, there are no pattern pieces on here yet because I'm not entirely happy with how the seat came out, but I'm going to make another one and upload something. I'll give measurements, though you should know that I did this a while ago and had to make a few drafts so I'm like 90% certain on a few of the pieces. I wrote things down, but then B "cleaned" and I can't find anything anymore.
So. Here we go. First you're going to start with these pieces. Clockwise from top left you have: arm covers (3" wide x 5 1/2" long), seat (3" x 3"), front (3" tall at the top of the arm x 4" wide), cushion back (roughly 4" long x 3" wide) and back (4 1/2" long x 4 3/4" wide). The arm covers are the main piece I'm not 100% sure on the sizing because I had to make them a few times. I know 3" is right but I had to change the length a few times. If the length is too long it's not really an issue; you'll see why in a few steps. Not pictured is the bottom, which will also be 3" x 3".
I made this mostly by drawing it on paper and sitting my animals on there to see how they looked. Draw the back and then you can get everything else from there; the front is the lower part including the arms and the cushion back is the upper part not including the arms. Kris's link has better pictures.
I interfaced most of my pieces because this is a lighter weight fabric.
Sew your arm covers to your seat, one arm cover to each side. I used a 1/4" seam allowance for the entire piece.
Because it's such a small piece, I found it a lot easier to keep track of what I was doing if I marked my sewing lines. I just used a pen. If you don't interface your piece you might want to use a fabric marker.
Now you're going to sew your seat/arm cover piece to the chair front. The best way I found to do this was to put my seat seams where I wanted them (in the corners), then pin the arm cover pieces working from the seat seams outward. This way, if your arm covers are too long the excess ends up at the outside bottom of the piece.
Clip your corners and curves.
Now, on the other side of the seat piece, you're going to sew your cushion back on. Getting the arm pieces to match up can be a little fiddly; here you can see that they're curved inward instead of outward like the front pieces.
Remember to clip your curves!
Here's what it should look like now.
Sew the back on. Here you can see how I did it: I pinned all my seams where I wanted them, then eased the arm fullness.
Sew the bottom on approximately 1 1/2 sides. You need room to be able to fit your armature in. You could leave just one side open, but I prefer to do a little more hand sewing and have an easier time of fitting the innards.
Now we make the armature. Since I wanted it to be washable, I decided to make it out of latch hook canvas. Just use your pattern pieces, making sure to remove your seam allowance. You'll need a back piece, a seat piece and a front piece. You could also cut pieces for the sides and bottom if you wanted, although if you do that you should probably only sew your bottom on on one side.
When I make the next chair, I'm going to try and figure something out to give the arms a little more permanent shape. I'm not sure if the latch hook canvas will bend in a curve this small, but muslin or light fabric could probably work. I stitched these together with thread, but you could also use yarn.
Wrap in batting and hand stitch it in place.
Test fit your armature. You might need to trim it here or there. You don't want it straining the seams.
Now stuff with fiberfill until you're happy with how it looks. I did the back first, then the arms, then under the seat. Just smoosh it around until you're happy with it. I like to pull my fiberfill apart as much as possible to try and get as few lumps as I can. Hand sew it shut and you're done.