Next time, a good idea is to use software such as TechTool and a cleaning diskette to clean the floppy drive.

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This is good advice. However, that won't get rid of the dust and old grease. Ideally you need to remove the cover and use a can of compressed air which should blow out all the loose dust and dirt. Then, using cotton swabs, you can clean any bits that are still left. It's also a good idea to oil or grease all the moving parts.