Feature List
As with any other product, you need to know why you are buying a digicam. This main reason will in turn affect the features you want your digicam to possess. Make a list of those features. For eg, if your reason was to take pictures for your personal website, you may be content with a 1.3 megapixel digicam. Even with the lowest resolution the pictures are great onscreen. BUT if you were to print that same picture, the results would be hideous! So know what you want before you get it.
Budget
When buying things there's always a budget (unless you are filthy rich). Work out your budget and stick to it. No point in getting an expensive digicam that's way over your budget just because it is the latest model and it has some additional feeatures (which you won't be using).
Battery Power
This might seem trivial but batteries are more important than you think. the type of battery used gives the digicam its final weight. It also dictates the duration of shooting you can do in one session. Some digicams can drain a set of battery in less than an hour of shoot! So be sure to check the battery consumption of the digicam.
Storage Media
Most digicam now rely on removable media (eg floppy disk, memory stick) for image storage. When buying a digicam, check if there's a free storage media in the bundle. It helps you save some bucks and kinda work like an incentive so that you can get shooting as soon as possible. Anyway, normally there would be at least an 8MB storage media FREE (actually 8MB is a really minute amount).
Compatibility Test
This factor is often overlooked. Check the compatibility of the digicam with your computer. Some digicams connect via a serial port, others via a parallel port, others via a USB port. If you have the right port and the slot is available, there's nothing to worry about. Otherwise, you might need to consider your options (maybe you'd like to consider getting a universal card reader).