When covering a scene in multiple shots, think "Wide, Medium, Tight, Repeat." Shoot a wide, establishing shot, followed by a medium shot, followed by a close-up. Change setups and repeat. The variety helps your scene flow and keeps it interesting.
Extreme close-ups can be extremely helpful. An XCU of someone's eyes or hands gives you the option of going to the next shot without the danger of a jump-cut. Use a tripod for these shots to avoid exaggerated camera jiggle.
A jump cut occurs when a person's position does not match from one shot to the next. For example, someone's hand is in his pocket for one shot, then at his side in the next. Stress to your actors the importance of keeping their movements consistent during multiple takes. Shoot cutaways in case you need them.
If shooting a scene where two people are speaking to each other, imagine a line running between them. You never want to cross over this imaginary line. If you do, the on-screen direction they are facing will be reversed, thus confusing the viewer.
Make your cuts while your subject is moving. The human brain is more forgiving of imperfect edits if movement is taking place. Small gaps or overlaps in action are not as noticeable.
Abrupt changes in audio can break continuity or unnecessarily draw attention to edits. Record a good length of ambient sound on location (traffic or crowd noise, chirping birds, etc.) that you can run continually in the background of your scene. This will help smooth transitions from one shot to the next.
Avoiding Continuity Errors
Casting Shadows with Cookies
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Mini Camcorders Vs Professional Size Camcorders
35mm Adapter Buyer's Guide
How To Video Record Live Events
Introduction to Digital Video Editing: The Guide to Getting Started With Computer Video (DVD)
Advanced Editing -- Guide to Advanced Computer Video Editing (DVD)
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Composition 201