More zoom, the better ! Many digital cameras come with both optical & digital zoom, which allow you to creatively frame your picture & focus in on distant objects. Optical zooms enlarge the subjects optically, using the cameras lens. Digital zooming samples whatever the camera is focused on and enlarges it, reducing image quality. In most situations it is not an issue (except for images intended to be printed in magazines/catalogues), and the benefits of digital zoom far outweigh any reductions in resolution. Best advice is to get to know the camera's zoom capability. 

Exposure compensation. Most consumer grade digital cameras will not allow you to set exposure time. However, you may have an exposure compensation feature, which allows you to over or underexpose your photos. This could be handy for taking some pictures under low lighting, or bright lighting conditions.

Take lots of pictures! Unlike conventional photography, digital photography has no costs associated with film, developing, etc.. So go nuts!

Read the manual. Know your camera's limits. Become familiar with all aspects of your digital camera's features. Experiment. This will eliminate fumbling to figure out a particular feature, perhaps missing the perfect shot!

Buy as much as you can afford. This isn't saying that you have to run out and spend $1000 or $2000 on a camera. But if you buy a basic one, it may not provide you with all of the features that you require! Having said this, there is nothing wrong with purchasing a basic digital camera, and upgrading as your needs and enthusiasm grow.