Do not go for power points in the early game! It is important to create a good resource base first. You should spend a few turns to try to get: infinite gemstones, science tokens, regular gemstones - in that priority order.
Go with the flow of the game. The easiest way to get points is by getting power and magic tokens. Consider more complicated options (tricky law cards, single-color bonuses, 5th pyramid level) only if they come around by themselves.
You should not use attack tokens during the game, unless you really need a certain card. Attack tokens are usually much more beneficial at the end of the game scoring, if your opponents do not have enough defense tokens.
Try to keep track of attack tokens that your opponents get. This will help you to avoid overspending for defense.
You should concentrate on getting as many points as possible during the second part of the game. It is important to notice the moment when you have gathered enough resources and are ready to score points.
It is easy to calculate how many points you will earn with your move. If you can get 10 points or more - it is a good move!
You may be tempted to play as many law cards as possible at the beginning of the game. Some of the law cards are indeed great for the early game. However, please note that most of the law cards are best for the late game or higher pyramid levels.