When you go to speak somewhere and you are offered a microphone, it's generally a good idea to use it. Keep in mind that the people running the event will be familiar with the venue and will know very well wether your voice needs to be amplified to be understood by the audience members in the back of the room.
You may be reluctant to use a microphone simply because you are not familiar with its correct use. It should be worth this small discomfort for the benefit of your audience, though.
Clip-on Mics and Headsets
Using a clip-on (lapel) microphone or headset is easy. It can be a bit awkward to put on, but the people offering it will usually be aware of all the potential problems (being too near or too far away from your mouth, where to run the cable to the transmitter, etc.). Once you wear it, you will soon forget about it.
A hand-held microphone can be a bit more troublesome, mainly because you have to be aware of it all the time. So when you turn your head but not your body, you have to remember to keep the microphone close to your mouth.
Usually, hand microphones are tuned such that you have to keep them very close to your mouth. In that case, a simple trick is to actually place it on the tip of your chin. For speakers with a beard, that would result in rustling noises, so you can put your thumb between your chin and the microphone to avoid that sound (thanks to Phil Waknell for that tip).
I've had setups where you had to keep the microphone further away from the mouth. Those require some discipline to keep it at just the right distance all the time. Don't be afraid to ask the technicians whether they can turn it down a bit so that you can use the above trick and place it on your chin. After all, it should be in everybody's interest to make things as easy as possible for both the speaker and the audience. Issues like this are one of the reasons why it's a good idea for a speaker to show up a little early so that you have time to test the microphone (amongst other things, like potential problems with the projector and your laptop).
The Cable Loop
In the end, it all comes down to practice. At a recent event, I was handed a microphone halfway through the talk (things did get a bit noisy outside the room and people in the back had problems understanding what I was saying). It was a hand microphone with a cable attached to it - something I hadn't used in a long time. A tip for those is to roll up a short piece of the cable in a loose loop around your hand; this loop then acts as a strain relief. I've heard that tip before, but didn't remember it at the time, which resulted in a bit of noise that the cable made when it came in contact with my body during movement. I hope it wasn't too distracting for my audience - and I will surely remember this for the next time now.
(Image Credit: Shure SM58 by Chris Metcalf, from Flickr)
Please email me for details.