Building an inexpensive paddle strop quickly
There are several styles of really nice paddle strops available at vendor sites, however they tend to be a little expensive. Here is a quick and easy design that you can build right at home. The process shown here will yield six paddles for less than $30, so that works out to less than $5 each. You can finish these in less than a day with just a few tools (a saw and a knife). If you don't need six and don't want to spend $30, then go by a leather shop and dig through the scraps. You might find enough for one or more of these for zip.
Building the strop
The secret for making this easy is to find leather strips and wood paddle stock that are already at the proper width. Here are some possible material for 1.5-inch wide wood paddles. The top piece is a paint stirring stick available for free at paint shops. The middle piece is a heavy-duty yardstick available for 60 cents each at HomeDepot. The bottom piece is a poplar trim strip available for about $3. These are all about 1/4 inch thick except the trim strip was a little thicker.
A look at the end grain. Top to bottom is the paint stick, the yardstick, and the poplar trim strip. The yardstick has a nice, tight grain pattern and looks quarter-sawn. Thus, it should be less likely to warp than the other two and give a nice stable surface for mounting the leather. This yardstick is much heavier than typical ones. Also, when you look for these, sort through the barrel to find a few with the best end-grain.
These yardsticks seemed to have a thin wash coat finish. It isn't much but it is better than nothing. This saves you from getting into a messy and involved painting or finishing process. The numbers and hash marks on the yardsticks are ingraved or pressed into the wood, but that did not seem to bother the leather surface when it was applied.
This is the contact cement that all the forum guides suggest for paddle strops. It works great. Spread it on both surfaces. Let it dry, and then carefully place the leather onto the paddle in the correct position and squeeze. No clamping is required. The most likely screw-up in this whole process is getting glue all over eveything. Don't get it on the top side of the leather!