Tuthill
The first things you need to decide are:
-What you're going to have the wine with
-What flavors you think you'd like (fruits, woods, et cetera)
-What price you can afford
There are certainly other considerations, but IMHO, food compliment, overall taste, and price would be my big 3 for a beginner.
For example, if you like pasta with red sauce, and want a stronger flavored wine, I'd suggest Chianti or Shiraz. If you want something a bit sweeter, maybe a white zinfandel. There are other choices that I'm sure other members will bring up, but the basic rule is whites (maybe blushes) pair well with chicken and fish, reds with beef and pork. However, if you don't like reds, drink whites or blushes with red meat! It's all in what you like!
For the above, I'd suggest trying Ruffino Chianti, Charles Shaw or Yellow Tail Shiraz, and Berringer White Zinfandel.
Try different wines by the glass at restaurants when you get the chance, and don't be afraid to ask the server for a recommendation. Be sure to note those you like and don't like! You can also find local wine shops that have tasting nights, and that's a great way to try different kinds!
Good luck!
Chuck