Battling in Clash Royale is like playing chess. There are different troops with different strengths and weaknesses.
The idea is to play your cards on their strengths and cover up their weaknesses using other support cards. If you get the combination right, you can 3-star any opponent.
The basic premise is this: Some troops attack in air, some attack both in air and on the ground. Some troops have high area damage and can be very effective for taking out enemy rush that has low hitpoint.
Skeleton army is a good example of enemy rush with very low hitpoints. It is recommended to use a Dragon, or a Bomber to subdue them. Make sure you don’t deploy the Bomber right in the middle of the enemy rush or he will be killed before he can take out the whole skeleton army.
For attacking, Prince is a very good choice. The Prince can cause great damage once it starts sprinting. It cannot attack in the air however, and your enemy might deploy minion horde to subdue him. Therefore, it is a good idea to pair the prince with a dragon or witch, both of which can attack in the air and have area splash damage. So even if your enemy deploys skeleton army, the dragon or which will take them out quickly and save your Prince.
Some of you might get lucky and unlock legendary cards in clash royale. There are two legendary cards in clash royale, Ice Wizard and Princess. Ice Wizard unlocks at arena 5, while the princess unlocks at arena 7. If you are the lucky few, you have a massive advantage over all your opponents.
GAMINGwithMOLT has an awesome tutorial video that explains all the basic attack strategies just right.