Tip 1: This is probably the most important bit of advice you can get and the one that will surely help you get a lot farther in the game. When aiming, don't start dragging your finger over the cue stick, but start dragging over the red ball. This not only helps you better visualize the trajectory, but also gives you more control over the cue stick itself. It sounds strange if you haven't tried it, and maybe natural for many. But I used to drag my finger over the stick when shooting and once I switched to dragging over the ball, I started scoring 10 extra times easily.
Tip 2: And nothing else. You don't have to make sure that the white ball doesn't get into the pocket, you don't really have to collect the gems, hit the other balls or send them anywhere. All that matters is that the red ball gets into the pocket - so that's your goal. Ignore everything else and only take them into account if they can help you reach your goal.
Tip 3: As you progress through the stages, sending the red ball to the pocket will get more and more difficult. Some levels seem impossible (they are procedurally generated so there might be hiccups here and there), but you should still do your best each time. Trick shots are difficult to pull, but always consider them: either send the red ball in such a way that it hits another ball on the way and changes direction to enter the pocket or go the even more difficult route and send another ball into the red one, aiming for the pocket. The direct hit is not always an option and, as the levels progress, you should definitely look into hitting trick shots and mastering them.
Tip 4: As you collect gems from playing (don't forget to also get your free Gem Hit every few hours!), you will unlock new items in the store, like new cue sticks and pool tables. They have no effect on the game though so unless you have a favorite one for whatever reason, you can simply select the dice from the menu which randomizes their use and offers variety throughout the game.
Tip 5: The more you play, the better you get at this game because you get to better understand the directions of the balls once you shoot. So don't let a bad run or low scores bring you down and keep practicing, always trying to anticipate the direction the red ball will see. Things will get better!