If you've ever wondered how to make a knife sharp enough to shave with, here's the answer: you need to strop it. Using a wet/oil stone will only take the process so far, as would a honing steel. This instructable will show you how to make and use a leather strop out of conventional household items: an old leather belt and toothpaste.

Step 1: Cut Belt / Wood Preparation

To Cut the Belt, Consider:

Use a paper cutter, they make nice cuts and go through leather well.
Alternatively, a utility knife works well if used slowly.

To Prepare the Wood:

Cut the wood so that it has about 1 cm margin (up to you really), I used a spare piece of softwood (not balsa!)
If you need to cut the piece in half, use an index card to find the center, it's faster than measuring.
Blunt all of the edges. An easy way is to rest a piece of sandpaper against one's leg or a couch cushion and to move the wood across it. I used my leg and 80 grit sandpaper.

The last picture shows the difference between an un-blunted piece of wood versus a blunted piece of wood.

Step 2: Make the Strop

To Glue the Leather:

Use any suitable glue. I used my wife's E6000 glue because it was specified to work with wood and leather. To apply the glue evenly, I only put it on one of the pieces of leather and then stuck the other piece to it. I squished the two pieces together and separated them.
Once the glue is applied, apply pressure to the strop with an even surface. I flipped the strop and pressed down on a flat paper cutting board.
E6000 is an evaporative adhesive meaning that it cures by drying. The volatile organic compounds (VOCs) leave it, causing it to adhere. To speed up the process slightly, I used a fan. Although this particular glue takes 48 hours to completely dry, I only dried it for 30 minutes before proceeding to the next step.

While You Wait:

Read some instructables.
Listen to some music LOUDLY at odd hours of the night, especially songs by Edvard Grieg.

Apply Paste Wax to Wood:

Cover the top of the strop with some blue painter's tape to keep the surface clean.
Apply paste was EVERYWHERE. Why paste wax? It's inexpensive, it's used to preserve leather, and it can be dried like the E6000. I waited 30 minutes before proceeding to the next step.
Pictured below is the the same type of wood with and without paste wax for comparison.
Note: if you don't want to keep throwing away paper towels or napkins, consider re-using remnants of a reusable bag or old socks for the paste wax. A small rag can be kept inside the container with the paste wax.

Apply Compound:

You ONLY need to apply whitening toothpaste to the leather strop for this instructable to be complete. I decided to make two strops because I happened to have some automotive buffing compound. If you have this, feel free to use it.
Why toothpaste? Toothpaste makes an excellent strop compound because it is slightly abrasive. Whitening toothpaste is even better because it is slightly more abrasive. To start, apply a very thin layer. You may want to add another layer after the first has dried.

Cover Strop with Paste Wax:

Conventional stropping compound is bound in wax, so to approximate it, I applied paste wax to the top of the strop, on top of the toothpaste.
Use your finger / a glove to apply the paste wax. This will prevent the paste wax from becoming contaminated. Also, don't use the same finger if you're using different types of compound.

Step 3: Sharpening Process

I like to shop at thrift stores and go to swap meets / flea markets. It's always fun to see what treasures you'll find. I found this case xx knife, which has a sturdy blade of surgical stainless steel. To sharpen it, here is what I did.

The sharpening stone was obtained at a local Harbor Freight store about $10 and is triple sided. Gray is coarse, green is medium, white is fine.
I'm not sure whether the stone is oil/water. To make life simple, I used a squeeze bottle to apply water. The water went right through the stone, unlike my previous silicon carbide stone so I had to water it with every swipe of the blade.
As with any polishing task, I started with the most coarse stone and a 7 degree angle between the stone and blade. I worked my way down to the toothpaste strop. With each change, I wiped the blade to prevent cross contamination. and increased the blade angle slightly. I think this method produces a sharp blade that is tough to dull, but does not slice through things as well as a blade made by keeping the angle constant. More comments are welcome as to proper technique since this is my first attempt at "proper" knife sharpening.

Honestly, the car buffing compound strop was too thick. Pieces kept coming off and the motion was not very smooth. I hope this goes away with more use, but I think just using the toothpaste strop ought to be good enough.

Step 4: Shave Yourself!

The ultimate test for any knife sharpening system is to see whether it is razor sharp. Is it? Yes, dull razor sharp, but still razor sharp! Here's how I tested:

Before picture, my left hand with hair.
Apply soap. Why? This is how I would do it with a double-edge safety razor.
Try removing hair.
Show a picture of the area and hair removed.

Great! This strop can make the knife razor sharp. Only in desperation would I shave with this knife. Maybe better sharpening technique would help?

Step 5: Cut Paper

Try cutting paper. It should be easy if you move the blade back and forth. It should be only slightly more difficult if you cut straight down without moving the blade back and forth.

Step 6: Practical Testing

I used oranges for testing because my wife and I have an orange tree in our yard producing too many oranges. Tomatoes would be better.

Qualitative Test:

Ultimately, a knife is used to cut food (in this case). The best way to check whether it works it see how easy it is to cut through food in thin slices. If it is able to create thin, even slices, it means that the blade is sharp and that it is also even. If it goes off to one side, then the blade is uneven. If too much pressure needs to be applied, or if back and forth movement is required, then the blade is still dull. I did not experience these problems with my sharpened knife.

Quantitative Test:

Being an engineer, a qualitative test is great, but I can't measure it. Why not something that can be compared? I have many oranges. By keeping the knife stationary and dropping oranges of comparable weight on it, two of the following can be measured:
Test A = Set the drop height to 1 foot: With different sharpening techniques, how deep does the knife slice? Record the results in a spreadsheet and compare.
Test B = Change the drop height: With different sharpening techniques, how high does the orange need to be for it to slice through completely?

The merits of each test are as follows: