There are three reasons why close-up pictures can appear blurry.
Yorky Lass and Dudley have covered the first one: Camera shake. As they've said, always use a tripod where possible. Otherwise, follow Dudley's advice to minimise camera shake.
The second reason for blurry pictures is simply that the camera is unable to achieve focus when very close to objects. Yorky Lass has effectively referred to this with her sound advice to look for a camera which features 'macro' mode.
The final one is 'depth of field'. When a camera is focussed on something, say, 8 metres away, anything between about 5m and 15m away from the camera might be in focus. (Actually, with the small apertures used by most digital cameras, that range could be far greater). However, the closer an object is to the camera, the smaller the depth of field. If the camera is focussed on an object 5cm away, it might mean that only objects within, say, 4.8cm to 5.4cm would be in focus. Anything else would appear blurred. Also, at such close ranges, a cameras auto-focus will either switch itself off or become unreliable. When taking close-ups it's really important to study the object in the viewfinder (or on the screen) to check that it's accurately focussed. If not, don't adjust the camera. Simply move it closer to, or further from, the object until perfect focus is achieved. (Yorky Lass's post also implies another good bit of advice: Don't just rely on a single shot. Take plenty, preferably from slightly different distances away from the object).
Chris