Trucks can be bought inside a Truck Shop, which is located at the bottom-left corner of the Main Menu. Trucks are divided by Tiers. Tap on Tier buttons to look at Trucks of the Tier you're looking for.
While choosing a new Truck be sure to choose it not only by its looks, but also by its performance. Take a notice at the Truck's Power Points (PP), which are located at the left side of the screen. Next to Trucks Power is its Tier. Note that you can use a Truck only in its Tier. For example, a T2 Truck can only be used in Tier 2. Below that you will find 4 main characteristics of the Truck.
Trucks can be bought with Silver or Gold. There are special delivery Trucks that can only be obtained from Containers, which are located in the Shop.