Well it's basically as simple or as difficult as you want to make it!
At it's simplest - crush the grapes and press out as much of the juice as you can get for white wine or leave the mushed up grapes on the skins to make red wine - only straining the juice off after a week or so. You can add wine yeast or use the yeast growing naturally on the skins of the grapes (which can be a bit hit and miss).
You can add sugar if you don't think your grapes are sweet enough to make a decent wine - but most don't.
The only thing to be really meticulous about is making sure that everything the grapes or wine touches from start to finish has been sterilised by heating (steam, boiling, baking the bottles in the oven) - or chemically (by soaking in sodium metabisulphite or another sterilising solution). Also keep everything covered at all times so that no nasties get in your wine - but bear in mind that the gas produced in fermentation needs to be able to escape - that's why glass jars with airlocks are normally used for home-brewing.
You can normally start it off in a clean bucket and worry about where you're going to strain it in to after a week or two has gone by - that should give you time.
Good Luck
It's fun!
