I've just watched Maze Runner and really enjoyed the story. I would like to know if I'll be able to continue to the second book just by watching the movie?
I suggest you read the first book before jumping into the second one. While most of the major plot points of the first book and movie are the same, there are many many things left out.
For instance, here are some things from the book that weren't on the movie: (Spoilers for the book)
1. Thomas remembers his name the moment he arrived at the Glade.
2. When Teresa arrives, she is in a coma for most of her time in the Glade. She only wakes up when the Ending begins.
3. In the book, when everything went wrong, it wasn't only that the doors didn't close. The sun disappeared and a grey ceiling-like thing appeared in place of the sun -- the sun was an artificial one
4. The maze isn't exactly same in the book. At the end of it, there is the Cliff. The maze simply stops and gives way to an abyss. The Gladers usually threaten to throw people off there
5. Thomas and Teresa can telepathically communicate
6. Alby is angry and not friendly
7. The maze showed lettered codes to the Gladers.
8. Gally was disappeared and later abducted
So, while you'll most likely be able to read the second book having watch the movie, I suggest you read the book.
(It will have you wondering what will happen next, even if you have seen the movie; not everything happens like it did in the movie)
The second film is COMPLETELY different to the second book the story line deviates. If you want to understand the second film read the Scorch Trials and the Death cure.
For example in the Scorch Trials book they are sent into the maze by Janson and they still think Wicked is good. In the scorch they meet Brenda and Jorge who are pretending to be cranks but are actually immune. The flare is a virus that is airborne, not passed when you are bitten. There are no doctors who reap children for their blood. Blood is not the cure and there is no cure to the flare. The immune are the only hope.
I hope that helps a bit more