Using a $5 or $10 bill is best, because the design on the reverse helps to hide where the crease is, and makes it much harder to figure out how to open it. This will work with any bill, but a newer one will make nice sharp creases.
Step 2: Fold one corner over.
It is important to line up the edges exactly so that the corner comes to a point (unfortunately, off the edge of the picture here).
Step 3: Fold the other corner over the same way.
This should give you a big X crease.
Step 4: Tuck in the edges and flatten.
Again, keep your creases sharp.
Step 5: Do the same on the other side.
It should be symmetrical.
Step 6: Fold in the ends of one triangle.
The points should meet in the center and just touch.
Step 7: Fold the top point down so it touches the other two.
Do the same on the other side.
Step 8: Turn the bill over and fold in the edges.
Note that this is the long edge that does not have the three points on it -- it is the side edge.
Step 9: Do the same with the other edge.
Straight edge, good crease.
Step 10: Turn the bill over again.
Everything should be nicely flat.
Step 11: Fold in the three-point end to the center.
Should look like this.
Step 12: Here's the secret step!
Fold in the other edge, and tuck one corner into the triangle on the other one.
Step 13: Tuck in the remaining corner.
It will take some slight fiddling, but be careful not to rip or crease the bill any more.
Step 14: Flatten it completely.
It should be almost undetectable as to how to get this apart without tearing it!
Suggestion: Don't do this on a regular basis with your own money -- it makes it a lot easier to lose!