Welcome aboard, Lori!
BASIC SLR TIPS:
1) Avoid the Green Box Mode. It's a fully automatic mode, to be sure, but in my experience it doesn't produce results as good as the semi-automatic modes.
2) As a beginner, I shot exclusively in P mode (program shift). P mode is a semi-auto mode. It measures the light and decides on shutter speed and aperture for you, but allows you to manually shift them. You won't need to do that yet, but in my experience, P mode does a better job of metering, resulting in better shots in most situations. Later, I explored the semi-auto modes Tv and Av, which allow you select either the shutter speed (Tv) or the aperture (Av), and the camera selects the other for you.
3) Practice Scott's "Da Grip." Nothing will get you better shots in low light without a tripod than a steady base for your camera.
4) Use the VIEWFINDER. You may be tempted to use the LCD screen to line up your shots, as you do with a point and shoot camera, but as they say in New York, Fugetaboutit! Pressing the viewfinder to your eye makes it far easier to see your frame than peering at an LCD, especially in bright sunlight; it saves tons of battery life because the LCD can be off most of the time; and it will make your shots far steadier because the camera will be braced against your head instead of floating in mid-air.
BASIC COMPOSITION TIPS:
1) The Rule of Thirds. Imagine if you will, that your camera's viewfinder is divided up by a tic-tac-toe board - three squares across, three squares down. Keep these lines in your brain at all times - and when you compose a shot, line up your subjects with those lines, instead of centering them. Picture of a lamp post? Don't center it, line it up with the vertical lines. Picture of the monorail? Don't center it, line it up with the horizontal lines. Picture of your kids in front of the Partners statue? Put your kids on the vertical line to the left, and the stature on the vertical line to the right. I harp on this one constantly, because it's the most basic technique of photography... that I constantly forget when I'm shooting my own pics.
2) ZOOM UP! Picture of your kids in front of Spaceship Earth? Zoom up so you can tell that it's your kids in the shot and not some random strangers. You can take wide shots of Spaceship Earth without your kids later, but when you want pics of your kids, you want pics of your kids. Likewise, if you see a cool feature like a statue or a topiary or a character, zoom up tight on it and forget the background. The background should not overwhelm or drown out the actual subject of a photo. Shoot people like Elvis on Ed Sullivan - from the waist up. Unless there is something about their legs and feet that is relevant to the pic, nobody needs to see them - but everybody wants to see peoples' faces in the pics.
Here's a nice example. Which of these looks better, the wide shot where he's centered, or the close-up where he's off-center?
Beyond that, have fun. Photography isn't about being good (I SHOULD KNOW), it's about enjoying the ride.