First things first, I've only made a few batches of wine, and I definitely prefer my home beer. However, I have heard that if you use your own ingredients - actual fruit, the wine tastes a lot nicer. However, here is what I do to make wine from kits.
You will need:
A demijohn (1 gallon, as opposed to the beers 5, as wine is a lot stronger). This is typically glass, but if you buy a plastic one they have caps and so you don't need to find a bung as well. Tl;dr, plastic is easier, glass just looks cooler.
A demijohn cork with a hole in if you have a glass container.
Silicon tube (there are similarities with my last list haha)
6 empty (for now) wine bottles and corks
And a hydrometer, cos wine is slightly more tricky than beer. A simple hydrometer is fairly cheap, comes with instructions and should be available from all brew shops/online/wilkinsons
Now for the actual making!
Pour the grape juice concentrate (from your kit) into the demijohn
Add ~ 3 litres/6 pints of cold water
If you have separate sugar, dissolve it in warm water. You shouldn't have to do this with most wine kits though
Add the sugar solution
Add water to fill up to 4.5 litres/1 gallon
Pour in the yeast
Jam in the airlock (with the little inside bit half filled with water)
Keep it in a warm room or wrap it up in a blanket and leave it for about a week
Now for your hydrometer - start taking readings. If you want a dry wine, stop at the reading .99-.996, for a sweet wine 1.009-1.018 and medium anywhere in between.
Now take out the bung, and leave the wine for a few days. It will slowly clear, and once it looks like wine should use the tube to get it into your wine bottles.
Cork them and your done!
Like the beer, the longer you leave your fresh brew the nicer it tastes, and this is doubly true with wine. However, even if you don't leave it, because you're a student and just want it for a party no one will remember anyway, it's fine to drink. Enjoy!