Is there a simple way to sharpen garden scissors without using a dedicated tool for that?
Sandpaper works for straight edged tools. A 120 grit or finer will take the little nicks out of the edge. Of course, regular sharpening and not trying to cut things that are too hard or too large means less work to sharpen.
For secateur and other tools with a curved blade any sharpening surface with a fixed edge works better.
There are any number of sharpening tools available for a nominal price which do a better job. This item has worked for me for five years on multiple tools.
You can pick up a rock and use that. If you find that some rocks work better, you're on your way to re-living the history of the natural sharpening stone industry in microcosm. It started with rubbing tools on rocks.
It helps if you understand edge geometry and what you should be aiming for - a tool like @kevinsky linked to takes much of the thought and skill out of the process, replacing them with mechanical constraints, which is convenient.
Without those mechanical constraints, you need to be thinking about and observing what your particular rock is doing to the blade, and what needs to be done to the blade to make it sharp, and manipulate things until one becomes the other. If that's not your idea of fun, the dedicated tool will work better, for sure.