I use Muriatic acid all the time. I've ruined my sink with it, btw.
To clean a tank, what I do is lay it on its front and fill it up with a 1/2" of water and acid (premixed in a bucket). Just let it soak for about 5 minutes, then clean it well. Flip the tank over and do the back the same way. Then each end. Then finally the bottom.
You'll use way less solution, and have less to pour out somewhere. I dump it out in an area that is basically dirt at the edge of my yard, since I like my lawn. If you pour it out on concrete, you may see a cleaner spot, since muriatic acid eats calcium and that is in concrete.
Wearing rubber gloves is prudent. If you don't have any cuts on your fingers, you can get away without using any, but you'll want to rinse your hands well and often. :shock:
Muriatic acid and water don't mix, so you'll need to stir it up well with a piece of PVC before you start.
Rinse the whole tank out with plenty of water. It will be fine. Dry it well, and it is ready to use. Acid lowers pH in a tank, in case you were wondering.
And FYI, about 5 years ago I was asking others how to get rid of Anemonia Majanos, and a couple of guys at MACNA told me I could inject them with muriatic acid. Yeah, in my tank. I ended up using boiling water instead, injecting that into them with a syringe. I just didn't like the idea of adding acid to my reef.