Muriatic acid in big box retail stores is already diluted, usually somewhere around 30% of full strength. The ideal dilution to etch a floor depends on several factors, so it's a good idea to run a quick test.
Clearly the first task is to be sure all safety precautions are followed. Use safety gear, no kids around, proper mixing containers, good ventilation, read instructions, follow them, etc. etc. Always have a large supply of clean water easily available to quickly dilute and wash off spills.
I first try a 2:1 ratio of water to acid, that is 2 parts water to one part acid. Note that you should always slowly add the acid to the water. Then apply a bit of the solution to an inconspicuous spot of concrete. What you want to see and hear is a small amount of interaction - a little fizzing, an bit of bubbling.
That would indicate that the acid is reacting with the calcium and other components of the concrete, however it does not react with other elements of the concrete. So where the calcium is dissolved by the acid forms small pockets, that's leaves a rough texture which provides more anchor points for the subsequent coating to mechanically grab onto. The acid also reduces the alkalinity of the concrete, which allows for a better chemical bound with some coatings.
If the text batch of diluted acid has visible "smoke" fumes, then the concentration is way too high. Whip up another small batch with a lower ratio of acid.
If there's no visible or audible reaction, that that ratio isn't strong enough for that floor, so try another test with a higher ratio of acid.
Eventually you'll find the right ratio.
When you apply it to a larger area there may be some spots where it still loos like nothing is reacting, use a broom with stiff bristles and scrub that area (be sure to confirm firts that the bristles aren't affected by the acid).
The acid will do most of it's work in the first 10 minutes or so. It will be largely neutralized by its reactions with the concrete, but it's still a good idea to use an additional neutralizing agent, like baking soda.
Do not allow the etching solution to dry on the concrete, that leaves behind that white residue (calcium carbonate) that people mention and that can effect the adhesion of the coatings.
It's probably pretty clear by this point that muriatic acid is strong stuff. It's very corrosive to metal, can damage landscaping, and can result in long term injuries and health problems if used incorrectly.
There are variations on muriatic acid, and even some other chemicals, that offer the same results, but have far fewer hazards and shortfalls. We supply an alternate etching chemical to facilities that can't tolerate the dust and mess that comes from grinding or shot blasting, and also can't tolerate the fumes or corrosive effects of muriatic acid.
Environments that fall on that list include zoos and other animal housing (zoos, research labs); hospitals, assisted living homes; electronic equipment assembly facilities, equipment rooms (power distribution, hvac etc.), or areas where the residents are sensitive/allergic to chemical fumes. A limiting factor to using those substitutes is they're more expensive.