For my Design Frontiers in Biology and Materiality class I experimented with spherification of edible liquids (and one pureed delicious solid). Given that you're on the internet, and can't taste my spheres, the next best thing is to check out the photos I took.
Spherification uses a reaction between sodium alginate and calcium to create a thin skin around the sphere. The liquid you want to create spheres out of is mixed with the alginate, and then dropped into a bath of water and calcium (I used calcium chloride). Reverse spherification uses those same chemicals, but, you guessed it, in reverse. This is necessary for liquids that contain calcium already, as they would thicken too much if mixed with the alginate.
I bought all my chemicals from lepicerie.com. If you're going to try this, definitely be sure to purchase food grade chemicals.
Liquids I made into spheres: Water, red tea, apricot nectar, apple cider vinegar, wine (pinot noire), Sriracha hot sauce, and pureed bacon. I reverse-sphered: coffee , balsamic vinaigrette, and milk.
I used a ratio of about 1 gram of alginate per 200ml of liquid, which in retrospect was a little much. Wine, for instance, thickened a bit more than I'd have liked, so while the spheres were tasty, biting into them was a bit more like eating an alcoholic gummy bear than a caviar. The tea and apricot didn't thicken as much, and had the desired effect. Bacon failed miserably and looked disgusting. Sriracha was so thick to being with that I diluted it some, but it was still to thick to form spheres in the air, dropped out of a syringe into the calcium bath: hence Sriracha spaghetti.
After dropping them in the bath, I waited about one minute, before removing them, and rinsing them in a water bath. This last step is important, because calcium chloride does not taste good. In the future, I may experiment to take them out sooner in some cases, to get a thinner shell
For the reverse-spherification I used calcium lactate gluconate instead of the calcium chloride, with the same ratio. It worked very poorly, as you can see here. The problem with the reverse is that, instead of a thin shell, you get a very thick, clear shell. This could be avoided with an decreased alginate in the bath, but that would probably necessitate a thickener in the spheres, such as xanthan gum.
A debate seems to exist about whether or not it's necessary to blend the alginate with your liquids, or just gently mix it to avoid air bubbles, as well as how long to wait do degas your liquids. I come down firmly on the side of an immersion blender, and learned that waiting to degas isn't that important, at least in my experience. Spheres with air trapped in them looked more visually interesting than the ones I degassed by leaving them in the refrigerator overnight, and had no disernable difference in texture.