It is simple really. Focus on one task at a time. Create a routine. If you are going to check and answer emails, then do only that until you are finished before you move on to the next task.
Here is what you do: Allocate an amount of time you want to spend answering emails. Turn off your phone, for example, so that you are not distracted. Go thru your emails, answer the most important ones first, and note which ones to follow up on, such as ones that need further research before you answer that email.
When you are done with answering emails, move on to the next task. Make this a habit and you will become very productive, efficient and effective.