Firstly if you already have a system like a Nikon or Canon 35mm with lenses stick with it, chances are you will be able to use some if not all of the lenses on your new digital camera saving you a small fortune! Plus some of the older lenses can be of a better build and image quality than some of the more recent offerings.
Right a step by step guide.
1. Decide what you want your camera for - if it is just taking shots of the family and the occasional outing stick with a compact camera or a prosumer model (looks like a DSLR but without interchangeable lenses) you will get better results from pointing and shooting. If however you have a partiuclar interest like Macro/close up, sports, landscape, portrait or wedding photography then a DSLR is probably for you. Now you need to consider that some cameras are better than others at certain disciplines. Canon are better sports cameras, Nikon are good all rounders and well built, Fuji are awesome for portraits and weddings, Olympus are good for travel photography thanks to their reasonably diminutive size.
2. Give yourself a budget and stick to it - factor in that you will also need at least one lens although ideally two. Get on to Ebay advanced search put your chosen camera in the search and look at completed listings over the last month - this will give you a good idea at what you should be aiming to spend. It will also give a good indication of a bargain.
3. Don't dive in straight away watch the market for a couple of weeks and see what your chosen camera is doing - be aware that camera prices can be changed by newer models or newer technology being introduced - it may be worth investing in a camera magazine like What Camera to see if your chosen model is due to be replaced - if it is hold off the price will surely drop as the new model is introduced.
4. Give consideration to the type of battery and memory that the camera uses - it might be compatible with memory and batteries you already have at home or that might be another cost for you. Generally DSLR's operate off either Compact Flash or SD.
5. Don't be lured into the megapixel battle - if you are going to be a keen amateur you don't need anything more than 6 megapixels which will blow up to A3 with some care. If you are considering going semi pro/pro then you will need at least 10 megapixels. Remember these cameras generally use different sensors than compacts so a Nikon D2H with only 4 megapixel will always produce better results than an 8 megapixel compact camera.
6. When buying be sure to check the feedback of the seller, don't buy from a new trader with 0 feedback its too much of a risk no matter how good the offer is, be wary of someone not displaying their own picture of the item and using a generic shot especially if its a used item. Be aware if you buy from China/Japan then you may be liable for import tax so factor that into your budget.
7. Generally these camera's are built to last especially Canon and Nikon so don't be scared of buying second hand - I have bought over 10 cameras second hand off Ebay and all have been fantastic and all have worked superbly as new. A good sign is that the used camera comes with its box and all of its bits and bobs it was originally sold with - this generally means that someone has taken care of the camera. Don't buy from a pro unless you know what you are doing they can generally be run into the ground. Most cameras are good for 100,000 - 200,000 shots so ask the seller if they know what the shutter count is.
8. As a first time buyer you should be looking to spend no more than £300-£400 for a second hand camera on Ebay, for that you can get mid range Canon, Nikon and Olympus cameras with a lens. Personally I would recommend the Nikon D70s with an 18-70mm lens. A brilliant starter camera that can take some pro shots. this also comes with one of the best kit lenses around. Remember this is a starter camera - you can always upgrade as you get better, but find a system and stick with it don't jump from Canon to Nikon to Olympus and back again it will ultimately prove costly.
So to sum up go buy a magazine decide which camera you want to go for and make sure its not just about to be replaced, then go and test it in your local shop to see if you like it. Then get on Ebay and check the completed listings to get an idea of prices so you can set your budget. Watch the cameras for a couple of weeks - don't panic if one goes cheap one week I guarantee another will go cheaper the week after be patient and make sure you understand your market a little before buying. Only buy from a reputable seller and make sure you check out the listing properly, have a good look at the photos and don't be afraid to question the seller. Finally don't forget to take into account all the other little costs like memory, batteries and cases....