If you have a SLR camera and it has a UV filter fitted to its lens, that's the first important accessory that you need to consider. If not only for the safety and protection of the front element of your lens.
There are many photographic accessories you can get for your camera, but you need to think about your budget and what you really need in the short term.How about your lens? Is it the one that was supplied with the camera as a package deal? If so, it probably has a good zoom range. The closer you zoom in on a subject, the more likelihood you have of getting blurred images as a result of camera movement. So a good sturdy tripod should be your next consideration.
See "Tripods and why"
When you study the manual that came with your camera, you will find there are a few optional accessories available for your particular model. The accessories that are usually supplied with it, are a cap for the end of your lens, where it fits onto your camera and one for your camera body, for when you remove your lens. If, when you do remove your lens, waste no time in attaching your body cap. The last thing you want is foreign bodies inside your camera.When you need to clean inside your camera, please refer to your manual for important cleaning instructions. There are appropriate cleaning kits available at good camera outlets that won't break the budget. (Please see “Camera Cleaning”)
One of the optional accessories will be a remote (cable type) shutter release. This, along with a good carry bag, should be your next consideration.
There are many other little bits and pieces that you could buy in the short term, such as a pocket torch, for night shooting, battery charger, extra rechargeable batteries, a large piece of plastic to cover yourself if it rains, or for a ground sheet for when you get down and dirty, or the more expensive extras like a flash unit and possibly a slave flash, and you will probably be tempted to acquire another lens for one reason or another, but I would advise you to get as much use and experience out of the one you have, before you even think about getting another.
However, later on, down the track, you might consider a Macro lens, for close-up work, or a longer lens for drawing your long distance subjects closer, or even an extra wide-angle lens for getting more of the scene in the shot.
For now, be content with what you have and work it to the bone!!!