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.
Quickest way of improving chess is
Playing lot of online games? OR Learning games played by GMs?