How can we finish an activity and alternatively ?
To finish an activity you need to call finish() Method of activity either manually or press back button which itself calls finish() method.
I guess you are asking about Android launch mode that can also be declared using the Intent flags, such as :
1) FLAG_ACTIVITY_NEW_TASK - If set, this activity will become the start of a new task on this history stack. A task (from the activity that started it to the next task activity) defines an atomic group of activities that the user can move to. Tasks can be moved to the foreground and background; all of the activities inside of a particular task always remain in the same order.
2) FLAG_ACTIVITY_CLEAR_TOP - If set, and the activity being launched is already running in the current task, then instead of launching a new instance of that activity, all of the other activities on top of it will be closed and this Intent will be delivered to the (now on top) old activity as a new Intent.
3) FLAG_ACTIVITY_SINGLE_TOP - If set, the activity will not be launched if it is already running at the top of the history stack.
More information of Intents is available in Android Developers website.
Also you can read a detailed description with examples in this link.
How to manipulate the activity stack with the help of Flags.
Manipulation of back stack depends on your requirement for e.g. if you want you see a certain activity later on after application starts then you can keep it in back stack Also if you do not want to see a definite screen for e.g. splash screen which is called only once needs to be finished while navigating to other screen.