The main objective of the game is to get all trainer badges. These can be obtained by defeating the Gym Masters from every city. Because of this, the only way to advance to another city is to beat the Gym master from the current one. The game will provide useful information along the way so it's advised to be aware. In addition, talking to people in a town could provide information that you can use. If you still are unable to advance through the game, you can search for a walkthrough on Youtube. There are plenty of these over Internet.
