I have found that success in online classes takes more than just staying on top of schedules and due dates. It takes an extremely organized individual that can focus on a milliion tasks at once, especially if enrolled in multiple online classes.
The first step to be successful in an online class is to make sure the class is something that you are interested in. If you are taking a class just because it fits into your schedule and meets a requirement for your degree, you may be in trouble.
Secondly, make sure you have allotted enough time outside of your other obligations to actually take care of the studying required for the class. This may come as a difficult task as some instructors don't give you an entire semester schedule at one time.
Finally, stay in contact with your instructors and keep them posted on anything that may be going on either within the class or things that may prevent you from getting assignments in on time (i.e death in family, change in work schedule, etc.).
Should you have no choice but an online class, due to requirement for graduation, work schedule, or any other obstacle in life, remember my second and third steps to get you through.