Pay careful attention to your power meter.
Keep in mind you only have a limited amount of time to take each shot.
Be very careful about playing hard and fast shots while there are still plenty of balls left on the table.
Play a soft angular shot that will give your opponent something to think about.
There are three power-ups you can use on the table: one will improve the aiming lines you're provided with, the next allows you to apply greater spin to the cue ball, and the third increases the maximum power available. You'll get a handful of these as you level up, but more are available to buy from the in-app purchase store.
In order to unlock new tables, you need to level up.
The game will warn you if you're about to hit an incorrect ball type by placing a red circle with a line through it over the target ball. Pay attention so you don't give away an easy free shot!
To add spin to the cue ball, first line up your shot, then tap on the white cue ball icon found in the top right-hand corner of the screen. Set the spin you want to achieve, then apply the power meter to take your shot.