Assuming you are talking about a barbers strop, you only use the smooth side.
One normally would go from a honing stone, to a canvas strop, to a leather strop. The leather only strops are meant to be used after a polishing stone like a Swatty. Strops are also not just a simple piece of leather, they have been highly compressed between rollers.
The whole meaning of stropping has gotten muddy over the years, and people get all fussy over the best way to use one - in some ways people who use strops are the worst of the sharpening crowd to claim to use the "one and only way."
I was shown how to use mine over 30 years ago by my retiring barber. Stropping is a swaging process, that forces the very fine scratches left by the stone to both flatten out and align perpendicular to the blade. No abrasion occurs during stropping. The blade must be moved fast enough, and with enough force to mold the steel. My barber said the main purpose of the canvas was to heat the blade from friction so the leather will work faster. I own a Swatty 3 line, so I never use the canvas. For what it's worth, a Swatty 3 line will leave a razor sharp enough to shave with right off the stone - the stone feels smoother than frosted glass.
Today, you will see many people charge a strop with polishing compound. Technically, this is not stropping since polishing is an abrasive process. Wood workers often charge leather to strop plane irons and chisels, and call it stropping. You can buy leather "stropping" wheels for the grinder as well. I do not get all wound up over people putting compound on a piece of leather and calling it a strop - I do however consider that to be polishing and not stropping. Polishing can be an extremely good way of getting a very fine edge on a cutting tool.
I suppose I should mention the issue with using any powered wheel on an extremely fine edge: The heat from a hard polishing or leather wheel will cause the metal on the edge to expand and compress. When the metal cools, micro cracks appear. This make for an excellent edge for cutting paper (paper cuts better with a very fine tooth if you draw the blade), but not especially good for cutting hair (or wood fiber for that matter). Carving tools can benefit from this since the edge is often rotated through the work, but plane irons like razors must cut with out sliding. Sliding a razor is in fact the easy way to get a very large slice on your face (you can actually push the wound closed, and continue shaving -it will heal with in hours and leave no scar).
All this said, a properly honed and stropped razor requires no effort to use. The weight of the blade really will cut off a beard.
I am sure that like dead vs live centers, other will have opinions as well.
