Of course with most digital cameras, you don't have much of a choice, so make do with what you have. This image of a small, but very colorful caterpillar was taken with a macro lens. The closer you can get to it, the larger it will be in the final image. A tiny coin surrounded by a large background isn't what you're trying to get. You're trying to get a large coin surrounded by a small background.
Macro mode is a special lens mode offered on some cameras.
Using this mode allows you to get a lot closer to the subject, making it much larger in the final image. Supplemental lenses may be available for your camera. Many point and shoot cameras won't have the screw threads needed to make mounting these easy, but you can carefully tape them on. If you can't get close enough to an object to fill the image area, you can always crop out the unwanted areas later. Just keep in mind that you don't have a lot of pixels to begin with and the more you crop, the lower the image's resolution will become.