Generally, there are two ways people hold their mobile devices when they are using them, including when they are playing games.
Two thumbs : This is when the device is in a landscape (horizontal) position and the player holds it using the fingers of both hands. Traditionally, only the thumbs are at the surface of the device screen, as only they can be used for various interactions. Such a position is inherent for various games with a dynamic content with less precision of input (large active areas should be used for more comfort).
One finger: This is when one hand keeps a device in a portrait (vertical) position and the other one is used for input: either single-touched (only an index finger is applied) or multitouched, when several fingers can be used at once, for example, gestures such as pinch.
Alternative scenarios are possible, but are less common and are used only in specific situations and cannot be considered as a prevalent behavior. For instance,...