Step 1: Ingredients
You need to end up with 180g of each flavor of Skittle. Since Skittles are approximately 1g each, you can accomplish this with 180 skittles. We used two 450g bags for our experiment -- other bag sizes are perfectly acceptable.
(Of course, if you want to experiment with making the vodka to be more flavorful, you could definitely try more skittles than this. This was what we found as a good flavor level, without using too many bags of Skittles.)
Can you use other candy with this same method? We think it's very likely that this will work well for most fruity candy generally available (like hard candies or chewy fruit candies). We're not sure how gummy candies would work with this -- but it's definitely worth experimentation.
The vodka quality is actually pretty important. We found that using middle-quality vodka created an end-result that tasted a lot like medicine (particularly the cherry flavor). I would suggest trying a better-or-best-quality vodka instead. Several commenters have pointed out that you can try running middle-quality-vodka through a water filter pitcher (such as a Brita) to clean up the flavor a bit -- we haven't tested this but it's worth a try.
We used one 750mL bottle for each flavor of skittle -- five in all. Larger or smaller bottles will result in more or less flavorful vodka for the amount of Skittles given above.
Step 2: To Start
Sort the skittles into different bowls based on color. We weighed ours with a scale to make sure we had approximately the same amount for each bottle (180 grams).
Remove and reserve a small amount of vodka from each bottle -- around 1/8th of the bottle.
Drop the skittles by color into each bottle.
Top off the bottles with the reserved vodka. (Enjoy whatever won't fit back in at your leisure.)
Give each bottle a good shake to get the dissolving process started. You should see the liquid begin to color relatively quickly.
Step 3: Waiting Period
Over time the vodka will begin to take on the color of the Skittles, while the Skittle bodies will turn white and start to break apart.
If you look at a package of Skittles, you'll notice that besides sugar and flavoring there's also a number of ingredients that give the candy its texture and chewiness. As your Skittles dissolve more and more, you'll get a thicker and thicker layer of white "scum" on the top of the liquid. This scum layer is pretty horrible and generally not tasty, so it needs to be filtered out before the drinking can commence.
Step 4: Filtration
The original method that we used for this was to run the liquid through a filter made of several layers of paper towels pushed down into a strainer. As several commenters pointed out, it is likely that coffee filter might be a better solution than the paper towels. We haven't tried this ourselves, but it sounds quite reasonable and we see no reason why you shouldn't try it.
It will take some time to get all the liquid through the filter -- be patient. The stuff left in the filter will be pretty gross. We couldn't think of a good use for it, so we chucked it in the garbage.
Step 5: End Result
You should end up with five bottles of relatively clear liquid. The purple will probably stay pretty opaque. The red, orange, and yellow will be pretty see-through. Green will most likely be in-between the two extremes.
There were some commenters who noticed problems with long-term storage of the purple variety -- they reported that over a period of days the purple color broke into a red with some blue mixed in. We didn't store our finished product for more than a day, so we can't speak to their experience, however, we don't think it's all that strange a result. The purple bottle was much cloudier than the others and we're sure they had to mix red and blue dyes to get that color to happen in the first place. You may want to drink this bottle quickly, rather than storing it long-term. (We liked the purple flavor a lot, so we didn't have any left after our tasting.)
So, how does it taste? We found that we liked the green flavor best of the lot -- it was probably the closest to the original skittle flavor and it mixed well with the vodka. Purple was a definite runner-up in the flavor contest. We didn't have any of these two bottles left after our tasting party.
Red tasted like cough syrup, which is pretty reasonable since it's a cherry + alcohol mix. Not our favorite, but if you like cough syrup taste, this is your winner.
Orange and yellow were definitely pleasant, without the cough syrup taste of the red.