Lectio divina is one approach. This article gives a good introduction about how to begin. (I had to condense it to post it; here's the link to the full text : http://floscarmeli.stblogs.org/archives/2005/11/lectio-divina-i-2.html )
Lectio Divina in Carmel and for You
by Steven Riddle
If you look at Carmel from the outside you probably would not be aware of one of its most open secrets... What is that secret? Well, the title of this entry gives it away--lectio divina... Lectio was not "invented" by the Carmelites. Likely it has existed in some form as long as there have been scriptures... I had never seen it as a particularly Carmelite tradition. But I have been woefully mistaken. Lectio Divina holds pride of place as the gateway for contemplation.
In Carmel, Lectio Divina or sacred reading, is seen as the root of any worthwhile mental prayer. One cannot engage in productive discursive meditation if one is ignorant of scripture. Ignorance of scriptures truly is ignorance of Christ. While we might not come to know and understand fully everything the Church knows and teaches about Jesus simply from reading scripture, the vast majority of what there is to know is centered there and stems from that special revelation.
**Lectio Divina is also a practice that has "methods" and a system. Further, it is a method that can be profitably employed by any reader...in relatively little time. Ten or fifteen minutes a day is all that it takes to start...Once you discover how simple it is and how utterly rewarding, the length of prayer time tends to increase on its own as you continue the pursuit of it.
Carmelites regard discursive meditation as the gateway to acquired contemplation... Thinking about holy matters can lead to a greater intimacy with God. Hence, thinking about sacred scripture--not in an academic or distant way, but in a highly personalized way--can open the door that leads to union with God (in God's own time of course.)
How does one "do" lectio? My guess is that there are as many different ways as there are practitioners, but I suspect that all of the ways include certain essentials.
After a period of quieting down (if done later in the day) and a prayer invoking the Holy Spirit one takes up scripture and reads. It is perhaps best if one does this according to a pre-set reading plan such as the Mass readings for the day or a plan to read through an entire book or section of a book...
After this quieting and prayer, one takes up scripture and reads... It is done slowly, as though weighing each word, or allowing each word to distill about it an image or a sense. It is better not to tax oneself with too long a reading... Perhaps a single pericope of scripture will suffice. Perhaps the next entry in the plan is dry and so two are entailed... [O]nce you start to really rejoice in the Lord, there is almost nothing that is too dry.
One reads a short section of scripture--savoring it, tasting it, chewing it over. In the words of Father John-Benedict Weber, sucking all of the juices out of it. (Don't worry--scripture is an extremely juicy fruit--even if you think you've gotten everything possible out of it, that is merely for the moment. Were you to return to the same scripture even the next day, you would be surprised at how deeply rewarding renewed meditation on it can be.) An important point to remember: lectio IS NOT Bible Study. This is not the time to be considering the parsing of Greek verbs or the economic relations of Syro-Phoenicians...Lectio seeks to draw out of the passage a meaning and a purpose that is personal in the sense of application. The end of lectio should be not so much a new understanding of the literal meaning of the text, but a new internalization of the text--a new understanding of how the text applies to oneself. As with all productive prayer, lectio should allow the practitioner to enter into a closer relationship with God. As the pray-er begins to internalize and make personal some of the truth present in the Gospel, a new way is forged to approach God.
It would be a very serious mistake to think that lectio is the work of the one praying. As with all prayer, its efficacy stems from the invitation, the grace God provides, that allows us to continue in it effectively. We do not produce the effects of lectio, but rather the Spirit praying within us shows us what we need to see in the course of our meditation.
Now, what form should this meditation take? ... One can form images and linger in the scene of scripture. One can hear over and over again a single phrase or word which has changes rung on it, shifting subtly and becoming progressively richer in meaning. One can begin to see all the strands that connect the whole of revelation and how this incident in a specific place is related to another elsewhere and hence, has ramifications for our lives today. The passage may plunge straight to the heart and convict one of sin, error, or fault. The key is to trust the lead of the Holy Spirit. He prays within as one reflects on Scripture. He connects one to the life of the Holy Trinity, and from within that life, one is given what is needed for the time. All stems from our trust and His Grace.
The method itself is so simple that one merely need take up sacred writ and start...Without lectio a Carmelite cannot reasonably hope to approach the contemplation to which we are called. Not everyone will enter contemplation in this way; nevertheless, it would seem a fine practice for any Catholic who wishes to know God as He knows Himself. That is, after all, what revelation is about.**