To a large degree caring for photography equipment is just common sense. The owners manual that comes with your camera should have good advice on caring for your camera, too.
Beyond the obvious suchas not taking your camera apart unless you're very trained in this line of work, not dropping it, installing the battery and memory cards correctly as per your owners manual and removing a leaking battery as soon as you discover it or if it starts to smoke, there are a few other things you may find helpful. Remember, professional camera repair people have ways of finding problems and damage that most of us could never, so use them when needed... They're probably worth what they charge, check their credentials.
If you do drop your camera assess the damage as best you can quickly. You may have to take it to a professional camera repair shop.
When cleaning the lens you should blow any dust or dirt off the front and back glass of the lens then breathe on it to create a fine mist that you will wipe off with a clean, soft, lintless cloth or better yet use a professional lenses cleaning kit made especially for this purpose... don't use any solvent or solution that isn't for this specific purpose.
Most cameras are not weatherproof or waterproof so you should carefully read the owners manual that comes with your camera to get more information about this. Also, store it in a well padded, weatherproof camera bag to protect it from the elements.
There are also lens filters that offer varying levels of protection for example from sun.
If you get caught in the rain or it starts to snow, cover the camera immediately. Some people put cameras in a clear plastic bag with a hole for the lense so that can continue taking photos in wet weather...you don't want the camera to get wet.
If it does, take it to a clean and dry spot where you can remove the lense, battery and memory card and let these air dry.
If you drop the camera into water, especially salt water, try to get it to a camera repair shop as soon as you can. If it air dries on route, turn it on to see if you can assess the damage some, this may come in handy when speaking to the technician who will be repairing it.
If you encounter extreme cold weather, try to keep the camera warm and any spare batteries warm too.
When you bring a camera in from the cold, the lens will mist up so let the camera air dry and warm some before going back out, you don't want the mist to freeze.
In hot weather, especially extreme heat, keep the camera out of direct sun exposure and don't expose it to the heat for very long periods.
While there are special cameras on the market like what underwater photographers use, the general rule for caring for photography equipment is to use common sense and read the owners manual. Learn all you can, expect the unexpected when it comes to weather and treat your equipment well, if you plan to get your monies worth and a lot of joy out of it.