Ask the LD student questions to determine if he understands an assignment or question you have posed to him. LD students may not provide the usual cues that indicate that they are listening or comprehending. Understand, before you undertake the task of tutoring the student, the specific nature of her disability and the obstacles it may pose to the normal give-and-take of a tutor-student session.
Embrace a multisensory approach, using visual (blackboard, projector, picture books) and auditory cues as well as verbal ones. Use props to make lessons more vivid. Introduce the student to mnemonic methods of memorizing subject matter. Present lessons in both written and oral form, using each to reinforce the other. For example, whenever you write something on a blackboard or paper, repeat it verbally.
Speak clearly and distinctly, at a rate and cadence that the LD student can follow. Without assuming that the LD student is deficient in intelligence, pace your instruction slowly and deliberately, so that you can be reasonably sure the student is taking it all in.
Encourage the LD student often. Your principal task is to teach the student how to learn, in order that he may one day be capable of self-teaching. Don't condescend to your student -- don't assume that she is lacking intelligence -- but reinforce her as you would any other student, with positive comments and by setting ever-higher goals.