"Google" the term, Lectio Divina, and you'll find numerous explanations on this method of reading and praying with the Holy Scriptures. 
However, one of the easiest-to-use methods among all of these is nicely explained by Fr. James Martin in this Video.

The method includes four basic steps, or questions to ask ourselves when reading 
a piece of scripture:
 

1. What does this text say? Meditation 
2. What does this text say to me? Prayer 
3. What do I want to say to God through this text?
4. What difference might this text make in my life? Contemplation or Action

Though its roots go back to twelfth century monastic rule, its use as a personal tool for lectors to better prepare themselves for their readings is invaluable.  When we can identify ourselves with the text and sense what God is saying to us in it, we'll be encouraged to listen to the readings at Mass more attentively. 

It is also important for lectors to keep the tone of a reading free from personal attachment so they can connect with a broad range of emotions and circumstances among the listeners.  

Aelred Rosser in his popular work, A Word That Will Rouse Them, notes, "The tendency we sometimes hear in readers to make the text individualistic or to shade it with their own personal application betrays an insufficient degree of objectivity and of sensitivity to the assembly's diverse needs." Where some arrive at Mass depressed or down on their luck, others will be content. Where some are in pain, others will be in joy; and lectors need to give everyone room to absorb a reading as their circumstances see fit.