Really basic questions

I'm really trying to get to take pictures, but sometimes I'm getting frustrated with camera shake (I don't know if thats the term, but some pictures get blurred), and lighting.

Well, the blur from the shake is hard to view using the camera screen, but I'm sure that the pics looks right or ok in lighting using the camera screen, but when I download them they're too dark. Is it that I should assume that the images as seen from the camera would be lighter than the final ones?

I have a Canon A520.

I see that your camera has a 35mm (film camera) equivolent lens focal length of 35- 140mm 4x zoom. the rule of thumb for hand held exposures is focal length equal minimum shutter speed, i.e. 1/35 sec shutter speed for 35mm, your lenses widest setting, 1/140 sec at 140mm, your lenses max tele length. Thats the rule of thumb, but scince your camera is fairly small its harder to hold still so you may be better off using 1/60 sec at the wide end and 1/250 at the tele end. You could do some test shots to find out at what shutter speeds your pics start to blurr for a given focal length.
For the second question check the images on someone elses monitor, if they still look too dark you may be able to adjust the LCD on the camera. Thats only a suggestion. depending on the camera settings every thing may O.K. You would do well to go to a camera shop or a knowledgeable friend for hands on help with this.

rzozaya-
Can you post a sample image here? That would help us evaluate the problem.

There are three basic causes of unsharp images: camera shake, motion blur, and bad focus

Camera shake is when your hands shake and cause blur. The longer the lens and/or the slower the shutter speed, the more likely you are to have a problem with this. When you're shooting outdoors in good light, this won't usually be a problem.

I'm guessing that your problem is actually motion blur. That's when your subject is moving and your shutter speed isn't fast enough to freeze the action. The solutions for motion blur are a faster shutter speed and/or panning so that you match the motion of your subject.

Can you please clarify so I'm sure what the problem is? No matter what, we can help :)