It can be hard to get your camera to focus on the main element of your shot if the object is tiny in comparison with the background. Manual focus is a way of getting round this problem, but point-and-shoot digital cameras rarely have a manual focus feature. So you'll need a little practice.
Focus the camera on something more substantial nearby - a leaf, for instance - and half depress the shutter button. Move your camera back in line with your subject and, still with the shutter half-depressed, slowly move towards the subject. Once the subject is focused on your screen, take the picture.
A tripod can be virtually impossible to use in macro mode because of the closeness of the lens. It will help the sharpness of your shot if you half-press the shutter button, wait for your shot to focus, then shoot. This will minimise shake. At such close range the slightest movement will ruin your shot.
If you're still getting blurry shots, you can significantly reduce camera shake by using the self-timer. This feature will help you avoid the hand movement that inevitably happens when you press the button to take a shot and it will allow you to brace the camera properly with both hands.
It can be difficult to know when to use the flash in macro photography. Ideally, you should never use it. If you're shooting a small object indoors, the flash will generally bounce directly back into the lens and cause massive glare. Instead try to illuminate the object with an external light source.
Using the camera flash outdoors can create problems, but you may need to on darker days. Try to shoot your object at an angle to avoid the light bouncing back at the camera. If you have the time, set up a tripod. Then turn off your flash and reduce the ISO level to allow more light through the shutter.
Even when you're 3cm from your subject, it's important to think about composition. Get as close as possible to your subject and fill the frame with your shot. But try not to have the main element in the centre every time. Some element interaction will make the shot far more interesting.
When you get close to your subject, the chances are you'll be blocking its main source of light. In harsh sunlight this isn't always a bad thing. Keep an eye on your position relative to the main light source and your subject. If you find yourself blocking essential light, reposition to suit the shot.