learn the basics: shutter speed, aperture and iso. all three control exposure, but each has different side effects based on usage
shutter speed controls the duration of an exposure. The shorter the shutter speed, the less time light can hit your shutter and the darker your photos appear. The side effect is that a short speed will "freeze" motion whereas a slower shutter speed causes motion blur, something you may experience in auto modes in the dark.
aperture controls the the maximum amount of light entering through the lens at any moment via a series of blades that come together to "stop down" and restrict light or come apart to let in more light. It's measured as a ratio of the opening to the focal length. The larger the aperture, the smaller the f number (ever notice people putting it as f/#?). The result is that you get more light in with a larger aperture and vice versa. The side effect is what is commonly referred to as bokeh. This is because some physics magic (circles of confusion and whatnot) cause out of focus objects to blur when using larger apertures. So that fancy portrait you got up there with the blurred out background probably was shot using a relatively large aperture.
last is iso. This controls how much the camera amplifies the signal from the sensor. The higher the amplification, the larger the signal will be and the brighter your image will be. Because you are amplifying a signal, there's always a chance for some noisy electrical interference to be picked up, hence digital noise. These are the weird blots of colors and dots that occur when you shoot in the dark, since the camera tends to automatically boost the iso if you shoot in auto.
learn how to use these three to create a nicely balanced exposure. Set a goal with each exposure and see to how to manage it. For example, when shooting in broad daylight, you're going to have a lot of available light. Whenever you don't have to struggle with a lot of light, you can set a lower iso to avoid that ugly noise. The rest is really up to taste. If you're doing a portrait, set a larger aperture (smaller number) and compensate with a faster shutter speed until your meter is about right. If you hit a wall such as the scene is still too bright despite max shutter speed of 1/6000 and 100 iso, compromise and give up a little aperture. getting a good exposure is all about balancing those three effectively
good luck! have fun playing around in the manual and semi manual modes, they'll help you learn a lot!