1. Determine how much you want to spend. Remember to include the cost of memory card(s), extra batteries, camera bag if required.
2. Are there any unusual features that you need? Waterproof/Dustproof? High quality movie mode?
3. Determine what type of batteries and Memory cards you want to use. Memory: Do you already own a certain type of memory for your old digital camera? You may want to be able to use the same storage and save a bit of money.
Batteries: Most digital cameras either operate on generic (eg. AA size) batteries or rechargeable batteries specific to the camera. Generic batteries Pros: Can be bought everywhere; each set is cheap; can use rechargable NiMH batteries.
Generic Batteries Cons: Always buying sets of batteries can get expensive if not rechargable; additional cost on top of digital camera; alkaline batteries may only last 1 shot in some digital cameras!
Specific Rechargeable battery Pros: Usually more power; Battery never needs to leave the camera; Some (eg some Sony) offer amount of time of battery life left, so you know how long you have til the battery dies.
Specific Recharable battery Cons: If you run out of charge, you need to recharge the battery or have an (expensive) spare; Lithium batteries slowly eat themselves, so after 5 or so years, regardless of usage, you will need to purchase a new lithium battery.
4. Weigh up the following factors: Optical zoom, number of pixels, size of LCD screen, Brand. The more you have of one, the less you can get for the others. A large zoom or a lot of mega pixels? Most pros would go for the better zoom. Secondly, weigh up pixels/zoom against LCD screen.
There is a growing trend to make cameras with larger and larger LCDs: 2.5″, 3″ or 3.5″. They make it easier to see the pictures you have, but they come at a price. Finally, the famous brand cameras typically produce better photos – its how they became famous!