There are about six things to think about.
1) Price.
You get what you pay for. Mostly. Under £3 per bottle is usually pretty dire. Over £8 is very rapidly diminishing returns. Very expensive wines are something of an acquired taste in my opinion. Watch out for muddle marketing though. One major high street chain massively put up its orices a few years ago and now sells on the basis of 3 for the price of two. Supermarkets love half price offers but when you taste the stuff it is clearly a £4 bottle being sold at £8 for a short period of time so that the £4 half price offer is legal. Be careful. Mail order from something like the Times Wine club or similar may be the best way to go. My personal sweet spot is the genuinly priced £5 to £7 range.
2) Coutry of origin.
Chile, Australia, New Zealand, South Africa, US on the one hand. More limited range of grape but very consistent. Personally I don't much like US or South African wines - can't put my finger on why though. I mostly go for Australian, New Zealand or Chilean stuff.
France, Germany, Italy, Spain, Portugal on the other. Massive range of diferent tastes. Some the best in the world, some appalling. Germany for sweet whites particularly. Portugal for port. France for champagne. Spain for mighty Riojas and sherry (Not Emva Cream or similar!). Wide range of grapes. Masssive, Massive range of tastes for such a relatively small geographical area.
3) The Grape.
Red: Cabernet Sauvignon, Shiraz (Syrah in France), Merlot, and many others with Tempranillo (spain), worth a special mention.
White: Chardonnay, Sauvignon Blanc, Chenin Blanc, Pinot Grigio to name some common ones.
Rose: Just a different wine making style using red and white varieties.
Note that there are dozens and dozens of different grapes, you can spend your life exploring them. Do a bit of googling for more info.
I almost always buy Shiraz, Merlot, Cabernet Sauvignon or Sauvignon Blanc these days. I have gone off Chardonnay.
4) The mix.
A £7 bottle of Cabernet Sauvignon based wine from Chile, Australi or France will all taste great, will taste a bit the same and somewhat different all at once. Find a country and region you like. This might take some experimentation and is fun.
5) Serving.
Wine goes best with food. If you sit in front of the TV and drink a bottle of Cabernet Sauvignon it will be nice. Drink it with a roast beef dinner and it is elevated to a new level. Somehow the flavours of the beef and the wine mix in your mouth and enhance each other. It IS a fact that certain wines work best with certain foods. This is not snobbery it is fact. Having said that most wine I drink is not with food. Most is in front of TV or Computer games. Some wines work better than others without food, ie quaffable is the word often used.
Chill if it needs to be chilled. About an hour in the freezer does the trick. Reds: Let it breath if you can bear to wait if it needs to breathe (Take the cork out and let it stand for an hour or so). Older high quality reds should breathe I believe - but I can't afford to drink those. Don't think it makes much difference really with younger mass produced reds.
A corked wine is one where air has got into the bottle over a long period of time due to a poor fitting cork, and the wine tastes vinegary, musty, mouldy and dead. It should be returned to point of purchase. It will be replaced without question. I haven't had a corked bottle for years.
6) You.
If you like it then you like it. If you hate it then you hate it. Don't let anyone tell you different. This is where wine snobbery starts.
Snobbery is not about describing wine as cigar box, melon, cirus, flinty etc flavoured. This is an attempt to give you a feel for the taste of the stuff. Other useful words are sweet, acid, heavy, light and so on. Snobbery is when some prat describes a wine as something like "Useful".
And finally - just go for it. Buy the stuff, Drink it and enjoy it.