The answer to your question is probably do nothing, as the system will do it for you.
It's important to note that the game (or any other app) will not simply run forever until manually closed. The Android operating system has built-in mechanisms for closing down apps which have been left running when their resources (such as system memory) are required by the system. In other words, if you start another game or other resource-intensive activity, Pokemon GO will most likely be shutdown by Android. It's actually recommended in most cases by Android that developers not manually terminate their applications, but allow the system to do it for them. (Emphasis mine)
In most cases, you should not explicitly finish an activity using these methods. As discussed in the following section about the activity lifecycle, the Android system manages the life of an activity for you, so you do not need to finish your own activities. Calling these methods could adversely affect the expected user experience and should only be used when you absolutely do not want the user to return to this instance of the activity.
This is probably why Niantic did not implement a back-button-to-close feature. All that being said, if you want to terminate the app because it's not refreshing properly (which happens often) the swipe method from the recent apps menu is perfectly acceptable and should not adversely affect your player data.