There is one simple set of knowledge that you need to grasp to use ANY camera, and once you learn the basics, your pictures will improve greatly. Most new camera users butch and moan about how this set of knowledge is not necessary with new electronic cameras . . . that they bought that fancy DSLR so that it could do all this for them, but that's a recipe for mediocre pictures, so here goes . . . learn this:
1. Aperture, or F-Stop. This is a hole inside your lens, usually somewhere in-between a bunch of complicated pieces of glass. You can make this hole bigger or smaller. Bigger hole = more light hits the photosensitive backboard . . . smaller hole = less light. On your lens (or in-camera sometimes), the size of the hole is communicated in numbers. IMPORTANT!!!! These numbers represent the bottom part of a fraction, so f2.8 is basically 1/2.8. f22 is 1/22. This confuses the heck out of new photographers, because BIGGER (f22 for example) numbers actually indicate a SMALLER aperture "hole", and therefore less light.
2. Shutter speed refers to the shutter, a "door" that opens to let in the light all the way to the photosensitive backboard when you press the trigger. When you set shutter speed, you are controlling the length of time the shutter will remain open before closing again. IF you think about it, as it is open longer, it is letting in more and more light. Now . . . shutter speeds are ALSO SET IN FRACTIONS!!!! So a shutter speed setting of 500 is actually 1/500, representing the 1/500th of a second that the shutter will be open. So again with shutter speed, BIGGER (500 for example) shutter speeds indicate SHORTER shutter times. One important thing about shutter speed: for handheld photography (not a tripod), the shutter speed should be almost as "fast" as the lens focal length you are using in order to avoid blur from hand shaking. So if I have a 50mm on my camera, I should use a 1/60th shutter speed or faster (in fact, much below 1/60th for handheld on wider lenses will blur as well.)
3. Shutter speed and Aperture must be adjusted inversely to maintain proper exposure (amount of light). Too much light and your photo will be too white, and brighter detail will be lost. Too little and it will be dark. Your camera should have an indicator of some sort to let you know what its exposure meter (think "light police") thinks of your current exposure. once you get the exposure close to acceptable according to the exposure meter, you can vary your aperture and shutter speeds inversely per your desired effect. Shutter speed effects your ability to freeze or blur motion (if it is open longer, fast motion will be capture dover that longer time period and will appear blurry. If it is open for a very short period of time, motion can be frozen or stopped with out blur.) Aperture changes your depth of field, AKA how much is in focus and how out of focus other stuff is. A bigger aperture opening causes much more blur in out-of focus areas. These two variables of shutter and aperture work inversely, so if you shorten the shutter speed by one step, you should open the aperture by one stop to keep exposure correct. Most of the time, you will be focusing on one or the other. If you are shooting sports, stopping motion is a must. If you are taking portraits, shallow Depth of Field is a must. in that case, set the important setting accordingly, then change the other variable to expose correctly. This is where the "S" and "A" modes on your camera dial come in handy. with "S", you set the shutter, and the camera sets the aperture for you. with "A" the opposite happens. I often prefer full manual, because it lets me fudge the settings slightly under or over exposure.
4. Notes
The other exposure factor is ISO, or ASA, or Film Speed (all the same thing). With a film camera, this indicates how sensitive the film is to light, with lower ISO being less sensitive, and higher ISO being more sensitive. On a digital camera, however, this is all done with processing. YOu should research good ISO settings for your camera model, as there are usually certain ISOs that are better. On other thing is the white balance (think color adjustment). Auto often works just fine for this, or the settings for different light sources (sun, tungsten, fluorescent, etc.) if you want to get fancy.
Also available are these filters called Neutral Density filters. essentially, they are tinted in order to reduce the amount of light entering the lens (here we are back on light again . . . surprise!) I personally use one of these that is actually variable (you rotate it for more or less tint) . . . because I do filmmaking, in which the shutter speed must be set specifically based on the frame-rate. This means that all I have left for controlling light is the aperture (which sometimes I want wide open) and ISO (which is constrained to the "good" settings). The filter gives me one more way to control light. They are expensive, but I find myself using it a lot, even for stills. It is nice having a big physical ring that I just grab and turn to change my light intake. It speeds things up a bit.
I BEG you, force yourself to use ONLY the manual setting on your dial until it feels natural to be adjusting shutter speed, aperture and ISO. Pay attention to the light meter, and adjust accordingly. Be thinking about the effects of your settings: are you stopping motion? blurring motion? Depth of Field? Once it feels natural and your mind is wrapped around what the shutter and aperture do . . . once it is instinctual, then star to think about using the "S" and "A" settings, and think more about ISO and white balance. Trust me, all those other dial settings are just bad automatic variants on "S" and "A" where you have too little control and too much is left up to the camera for you to get consistently good pictures.
As far as advice, I say buy a good 50mm equivalent prime lens that has a fast aperture. The lens that comes with your camera is guaranteed to be meh. Hock it off and get a better zoom if you must have a zoom, but primes will be better quality in general. Avoid unnecessary equipment like flashes, lights, etc. They're just going to mess with your light and your mind.