How to sound more professional: learn to omit filler words

"Hmm", "I mean", "like", "uh": all these are typical filler words and many people use them to a greater or lesser extent when talking to colleagues, managers, clients and subordinates. Some people's use of such fillers is so prominent that those around them can hardly focus on anything else. But even if your filler words are less obtrusive, they still have a subconscious impact on your listeners, who then regard you as less confident and professional. How can you stop using these fillers and sound more professional?