Start using a commentary in your Bible reading, such as Kretzmann online. Even better would be using the People's Bible Commentary Series from Northwestern Publishing House, though.
Here is Kretzmann's take on the verses you are talking about:
Christ's advice to the tempted: V. 29. And if thy right eye offend thee, pluck it out and cast it from thee. For it is profitable for thee that one of thy members should perish, and not that thy whole body should be cast into hell. V. 30. And if thy right hand offend thee, cut it off and cast it from thee. For it is profitable for thee that one of thy members should perish, and not that thy whole body should be cast into hell. The right eye and the right hand are named as prominent members in the actual committing of sin, through which the evil desire of the heart finds its expression. They are represented as the organs of temptation. According to popular view, they are the members that offend, that incite to the actual commission of sin. Therefore, symbolically speaking, these members and all the members of the body must be controlled, if necessary, by an absolute and painful renunciation. Better to be without individual organs and members of the body than have the whole body condemned. Christ speaks figuratively, and His words must be understood in the spiritual sense; for mutilation evidently may prevent the outward act, but will not kill the desire. Every member of the body shall be so controlled and governed by the sanctified will that it will not yield to sin, thus bringing the whole body into condemnation. Jesus again uses the figure of the perpetual fires of the valley of Hinnom, where the waste and refuse of the city of Jerusalem was burned, for the punishment of hell. "This, then, is the meaning: If you feel that you look upon a woman with evil lust, then pluck that eye or vision out as being contrary to God's commandment, not of the body, but of the heart from which the burning and desire proceeds, then have you torn it out rightly. For when the evil lust is out of the heart, then the eye will also not sin nor offend you, and you will look upon the same woman with the same eyes of your body, but without desire, and it will be as though you had not seen her. For no longer is that eye there which was there before, which is called an eye of burning or desire, although the eye of the body remains uninjured." 51)