Quickest way of improving chess is

Playing lot of online games?   OR   Learning games played by GMs?

Playing your own games is the best way to learn.

However, I suggest you also watch some top-rated games in live chess.  It's an awesome feature, and you can see how good players duke it out.

I also find it helps to read up on some books, such as chess fundamentals by Capablanca.

If you are considering watching other peoples games I have found that it is usually better to see games  of players rated about 200-400 above your own current rating.  Any more than that and you probably miss half of the theory behind their moves.