As with all these designs, try to start with a relatively clean, crisp bill. It will make it much easier. All folds should be sharply creased. It helps to go over the fold with a fingernail on a flat, hard surface.
Start by folding the bill precisely in half lengthwise. (I prefer to fold in toward the front of the bill. I think it produces a nicer design on the end product. For your first attempt, it will be easier to follow exactly the same orientation on the bill as shown in the photos.) Unfold the bill, leaving the crease produced by the fold for the next step.
Fold the bill one quarter of the way in from each side lengthwise. The edge of the bill should just meet the crease made by the fold in the previous step. Do this for both sides as shown.
Turn the bill over. Fold the white of one end over as shown. This will become the collar in the next step. (If the bill is printed unevenly, use the wider edge.)
Turn the bill over again. From this side, angle-in the two corners from the end you folded in the last step. The two points should meet precisely at the centerline. The angle is not terribly important, but should be about the same as shown in the photo.
Fold a little less than one third of the bill lengthwise from the opposite end as shown. If you're following in the same orientation as the photos, use the markings on the bill for a fold point. (Notice that the edge of the bill just meets the word "OF" on the reverse printing.) If you fold too little, the shirt will appear too long in the end. If you fold too much, the next step will not work. See below.
Now you will fold inward in the same direction, tucking the previous fold under the "collar" created in step 4. So far it looks kinda 'nifty, and if you know it is supposed to look like a shirt, you get the collar concept. But wait, there's more...
Gently unfold the previous two folds, keeping the creases. On the lateral fold furthest from the collar, refold it strait across as shown. (On the flatbed scanner, this made a bit of a mess of it, but it is fairly easy in 3D.)
(This step is hard to describe, but it is actually fairly easy.) You are going to introduce two new folds on each "sleeve". I do this by holding each side of the previous fold between thumb and forefinger in the orientation shown, just on either side of the vertical fold as shown. Just force the angle to close slightly, and force the extra paper inside the vertical folds. Once you've got it looking right, force the insides to crease by pressing on a hard surface. (Try looking at the next photo - like I said, it is hard to describe!)
(This is a close-up of what the fold should look like when complete.) Do this for both sides.
(This is what it should look like after both sides are complete.)
When you re-tuck the fold you've been working on back under the collar, you're done! It should look about like this. With the basic shape, the collar and the sleeves, it should be recognizable. Once you've done a few, you can try folding the whole thing into the reverse side, leaving the obverse side out. (Like I said, I think this looks better. This is especially true with 1 dollar bills where the edge seal on the reverse under the collar looks a little bit like a necklace.)
The Boots
These boots were made for (when your fingers do the) walkin'
Each boot takes one bill, so you'll want to start with two dollars so you can make a pair of boots.
As with all these designs, try to start with relatively clean, crisp bills. It will go much easier. All folds should be sharply creased. It helps to go over the fold with a fingernail on a flat, hard surface.
Start by folding the bill exactly in half lengthwise, shown at top.
Then, fold unevenly end-to-end, so the ends miss by about one half of an inch.
Ease open the end-to-end fold, (retain the crease, you'll reuse it later), and make the lengthwise fold meet the end-to-end fold line. (The bill's border should be out away from, not in towards the fold.)
Now fold the other end in toward the same line.
Note how this looks. The white borders around the edge of the bill are away from the last two folds you've made.
I'll refer to the vertical line where the two meet as the centerline in following steps.
Fold both outer edges in toward the same centerline, from the same side.
(Okay, the picture is a little screwed up. The one on the left has both folds, the one on the right has only one new fold.)
Without unfolding anything, fold the shorter of the two ends away from the centerline. Repeat this two more times until it looks like the close-up picture shown. (Simple to do, difficult to describe.) The idea here is to make that end smaller, so we can tuck it in a tight space a couple of steps from now.
Take the longer tab, and make a bend so that it passes underneath the shorter end. The edge that was the far left edge in the previous picture, and is now the horizontal line in the current view should be at a ninety degree angle with the centerline.
If you refold the centerline fold, you're here. (This picture is rotated relative to the previous picture. The centerline fold has become the top edge of the lower/front portion of the boot.)
Now take the shorter, pointier loose end and wrap it around the heel area of the boot.
This is the bottom view after tucking the short end in. (Okay, look at the next picture for where to tuck it in.)
Once tucked in, you are nearly done. (Optionally, curl up the toes for the "elf boot" look, as shown here.)
Open up the folded top, and stick your finger in. Just apply pressure where needed to open up and round the upper portion of the boot. In this rear view, you'll notice that you just have to "smoosh it" towards the bottom rear to get it looking right.
That's all there is to it. If you want to make a symmetric pair, (shown) alter which side is long and which is short from the second step, and follow the same instructions, reverse left for right.
The Ring
As with all these instructions, try to start with a relatively clean, crisp bill. It will make the process easier. All folds should be sharply creased. It helps to go over the fold with a fingernail on a flat, hard surface.
For your first attempt, use a 1 dollar bill, as the description is based on the features of the reverse face of that bill. After you've done a couple you can try out different denominations.
Start by folding the white border (no more, no less) at the top and bottom of the bill toward the obverse (front) side. The picture here only shows the end, but do this evenly down the entire length of the note.
Fold the bill precisely in half lengthwise, twice. If you've folded very carefully, the ONE insignia will be evenly framed top and bottom, and the width will be even along the entire length. 
On one end, fold the white border at the edge back. Fold on the other side of the ONE insignia so that it is evenly framed in a square as shown. (The lower picture shows this fold purposely folded skewed to help you see what I'm trying to explain. Make your own folds as precise as possible.)
To simplify the description in the following steps we'll call this end of the bill the head. The other end of the bill will be called the tail.
Start curving the bill away from the head as shown. Pay particular attention to the direction of the curve relative the folds made in the head. (If you curve the wrong way you won't be able to complete later steps.) It sometimes helps to 'rub' over the corner of a tabletop or similar surface to get a nice curve out of a stiff bill.
Next make a 90 degree bend in the bill as shown. Where this bend is made will determine the size of the ring. The further from the head, the larger the ring. (The curve from the previous step is flat in this picture because of the scanning process.) Once you're used to making these, you can wrap the curve around your own finger to estimate the correct position for this fold. For now, just use the picture for a guide.
Now wrap the tail tightly around as shown. (In this picture the portion to the left is shown in the same position as in the previous picture, and the tail folds underneath.)
Using the curve created three steps above, Loop the head back around to a position on top of the 90 degree bend made in the previous steps.
Continue wrapping the tail around the body of the ring until all the excess length of the tail is used up. If you've followed the previous steps closely, the very end of the tail will be on the outside of the ring (under the bend in the head).
This picture shows the tail wrapped all the way around and the head at the top of the photo. Using your fingernail (or anything else convenient, I use a key most of the time), spread the gap between the wrapped portion of the tail and the body of the ring. In this gap, tuck the last fold in the head.
These two photos show the finished product. This also works well with 10s and 50s. 5 and 20 dollar bills work, but require a bit of adaptation due to the difference in size and position of the denomination insignia in the corner of the bill. Work with 1s and 10s until you get the hang of it.
