Gain basic knowledge of the faith
Before embarking on a study of the Qur'an, it is necessary to have some basic background in the faith of Islam. This will give you a foundation from which to start, and some understanding of the vocabulary and message of the Qur'an.
Choose a Quran translation
The Quran was revealed in the Arabic language, and the original text has remained unchanged in that language since the time of its revelation. If you do not read Arabic, it is necessary to obtain a translation, which is at best an interpretation of the Arabic meaning. Translations vary in their style and their faithfulness to the Arabic original.
Choose a Quran commentary or companion book
As an accompaniment to the Quran, it is helpful to have an exegesis or commentary to refer to as you read along. While many English translations contain footnotes, certain passages may need extra explanation, or need to be placed in more complete context.
The Quran challenges the reader to think about its message, ponder its meaning, and accept it with understanding rather than blind faith. As you read, feel free to ask for clarification from knowledgeable Muslims.
Continue to learn
In Islam, the learning process is never complete. As you grow in understanding of the Muslim faith, you may come across more questions, or more topics you want to study. The Prophet Muhammad (peace be upon him) told his followers to "seek knowledge, even unto China" -- i.e. pursue your study to the farthest reaches of the earth.