5-10 minutes of soaking in muriatic acid results in a fairly even texture on the surface. Can soak longer if you dilute the muriatic acid. Full strength from the pool store (34% I think) tends to boil quite strongly and may spill out, diluted will fizzle in a much more controlled manner. This step can release fair amount of heat, i.e. if you do it in a glass container, that may crack, or the aluminum part itself will become hot to the touch. Although should still be ok to handle, aside for obvious contact with the acid itself.
Here is an exemple of just dripping a bit of acid on the surface. The reaction does not last too long as the acid gets used up in 2-3 minutes. This can be used to add local stains/patterns.
Example of a pattern. Printed a logo on a piece of paper, attached it to a blue masking tape, and cut it out. If you have double sided tape that would work better, I just used some tacky glue to attach the cutout afterwards. Then I just poured some acid over the top. It seems that for some reason it ate away aluminum right at the edges of the logo.
Full bar of aluminum that I have been playing with
After all acid treatments I've used 400 grit sandpaper to give it a good scrubbing. So at this point the surface is pretty much finished and won't mark your hands with aluminum oxides etc. Everything feels very smooth, just not shiny. I imagine with higher grit papers that can be achieved to a point.
Full size images can be seen if you click them.