I have never tried dandelion wine but I have heard it is somewhat comparable to mead (which I do enjoy) and may even have a honey taste. There are many variations to making dandelion wine, some with more citrus, some with more raisins and other dried fruits, so let me qualify this one by saying I have never made it and provide no guarantee it will be something you want to actually drink! :-)
There are many websites dedicated to wine making and I recommend you visit such a site before taking on this project. It seems like a little bit of knowledge will help guide you through this process rather easily. Some of it has to do with individual preferences, and other aspects deal with the fermentation process. In a nutshell, you are going to make a dandelion tea, then add some fermentation food (yeast), and set your brew aside for a while as it turns into wine. I will try to provide a bit of information here, but again I recommend reading up on home brewing if you really want to try this. You also need to identify a location where you will leave your brew to ferment for several months to a year. In the old days, it might have been a root cellar. Consider a location that does not have wide fluctuations in temperature based on the seasons.
Dandelions seem to grow all the time but they are most prevalent in North America in spring and summer. Try to harvest flowers that have not been sprayed with an herbicide or pesticide, and harvest them in the midday so the flowers will be fully opened. I will add some more directions after the recipe, in italics.
4 qts dandelion flowers
12 qts boiling water
Let it stand for 24 hours then strain through cheese cloth
4 lemons, add juice
4 oranges, add juice
1 lb raisins boiled 1 hr then run through seive add juice wine and 10 lbs sugar
1 cake fleischman’s yeast dissolved in warm water
Use sunmaid raisins
Day 1 – harvest and clean your dandelion flowers by washing and removing all green parts, ideally leaving only the petals. Add to boiling water. Let stand 24 hours.
Day 2 – Strain flowers through cheese cloth and discard them. Juice the lemons and oranges ensuring there is no pith in the juice. Add the juice to the dandelion liquid. Boil the raisins and strain them, discarding the fruit. Add this liquid to the dandelion liquid, as well as the sugar.
Let the mixture boil at a slow boil for 1 hour, then let it cool. Pour it into a winemaking vessle, such as a jug and add the yeast. Let it set for three days then strain into a second winemaking vessle. You will then need to secure the opening to ensure no unwanted yeast spores enter the bottle while it is turning into wine. Some sites suggest a balloon with a few small holes pricked into it. The wine should sit for three to six months and will need to be strained into another bottle at least once.