When you start, you're brought to level one. At the bottom of the level are tower spots. Here you can build towers to shrink the balls.
If you tap on one, a menu will come up showing available towers. If you are just starting out, only one tower is available, the Gun Tower.
Ignore the book and tap on the name of the tower to build it. Do the same for the rest of the tower slots. Your towers will go to work and start shrinking balls
If your balls get stuck, you can clear the balls in the settings menu.
Once you have 10 coins you can upgrade your towers, click on a tower and pick an upgrade (damage is a good idea). This will apply to all your gun towers, but it's reset on prestige. Once you have shrunk 25 balls, you'll have made 50 coins, enough to earn an upgrade point. Upgrade points are used to apply upgrade and purchases that will persist until you respec.
Click on the prestige button and select the top option "Prestige". The game will start over and you will now have a prestige point. If you click the crown on the bottom right, you can see there are options to select, select the gun tower.
If your just starting out, it's a good idea to upgrade the max targets, since this will double your damage output. Once you spend a point, it's applied immediately. Notice that when you spent the point, the costs for all the other upgrades increased. For each upgrade menu, the costs for the upgrades will increase for every purchase. Now, if you build your towers again you can see that your towers are shooting at two balls at once, making them much more effective. This is the basic gameplay loop. You should explore the upgrade menu, note that the first gun and general purchase only cost one point each. It's recommended to get the bomb tower and unlock level two next, so you can shrink more balls and earn more prestige points.