How difficult is it to purchase Premier League Soccer Tickets?

It depends which city you are hoping to watch a match in. If you want to see a game in anything other than the Premier League you would have no problems even on the day of the match. The Championship, the level below the Premier League is of a good standard played in decent stadiums. However if you want to see any of the "bigger" teams in the top league you would be lucky to buy a ticket legitimately on the day of the match particularly at the London grounds. There would be agencies who sell tickets at a price and of course touts (scalpers) outside the grounds. This is not a recommended option and at your own risk as the ticket could be a forgery. The club I attend (Southampton) does usually have a general sale of tickets for most games a few weeks before the game but clubs often operate membership scheme. Look on clubs' websites. If you want a London game West Ham would be a good choice. Not a great team but a historic club who provided the backbone of England's only World Cup winning team. They play in a stadium in the East End although are moving in a few years to the Olympic Stadium. You would have a very authentic experience in comparison to a sanitised atmosphere at Chelsea or Arsenal. In addition they often seem to be advertising their games for general sale.

Thanks, David, for the advice! Got to see York City Football Club play against R. United. York City F.C. field is down the street (about 3 min walk) from the Amber House B&B, which is where we were staying. Loved the fun atmosphere at the match! Oh yeah, we got tickets the day of the match, and they were inexpensive (12 pounds each for reserved seating).