The patina effect can be accomplished in many ways from heat to acids to commercial products, to simply leaving it out in the rain or baking it in the sun with household chemicals, using vinegar, pickles, salt, you name it. Watercolors and inks can be used too, but obviously those aren't true patinas.

Be careful mixing chemicals, bases, and acids. For example, if using ammonia, don't mix with bleach. Heating chemicals can also increase an effect but may also release poisonous fumes, so ventilate well.

Get the mindset to be patient, go slow and don't overdo it with the patinas. Know that the weather of the day will affect the heating and patina effects so a cold humid day may yield different coloring than a warm dry day vs a warm humid day vs a cold dry day. Wind blowing, ventilation fans running,... you get the idea.

If using a propane, oxy/propane, or oxy/acetylene torch on the metal don't spend too much time in one place, and if already installed, move around a lot to avoid burning the surface underneath.

I suggest laying the copper out on a temporary frame OUTSIDE since patina chemicals can smell bad, release fumes, make a mess, etc.. then work your process.

So, as you can imagine, there is no need to prop the copper - you can work it while horizontal or even after installation. Copper may warp so go easy on the heat but I doubt that will be of much concern at 24 gauge (16 oz). If you want to go crazy with the heat, find even thicker copper.

While you're at it, work a second piece of copper at the same time for your ventahood, wallplates, sconces, or whatever, so they look similar in nature. Using the same chemicals and weather conditions can yield similar color variations in your work and tie it all together.

Allow the copper to breathe for a day or two if shipped in to compensate for temp/himidity/weather and find out if you need to clean the copper if the manufacture put a protective spray on the copper or if plastic laminate protects the copper, peel it away before beginning your process.

When you are ready to get started, try a test piece before you work on the full counter top so you can see how extensive the patina effect will be. Don't be afraid to experiment as all results will be unique. 0000 steel wool can be used to remove minor mistakes.

When finished, if you don't seal the copper, the copper will continue to discolor and change over time, a very cool effect sometimes, but know too that some patina effects will wipe off if not protected.