A couple of people have asked me questions about "how to". 
So, I'm going to try and break this down to describe what I do.  Now please keep in mind that I'm an amateur.  I don't do fancy things and I really try to do things as easily as possible. 

1)  Camera -  Almost self explanatory, but I want to cover a few basics.

• Optical zoom is the only thing that counts.  Ignore the digital aspect.  Many cameras try to sell the consumer on their digital zoom.  Digital is simply artificially enhanced zooming.   What they do is take the optical zoom and use a multiplier.  If a camera has a 3x optical zoom and the digital is a 10 --- their advertising will read 30x digital zoom!!!  Ignore that.  Only pay attention to the optical portion.  If you can get a camera that has a high optical zoom.. GO FOR IT!  It's a good thing.
• Megapixels are important.  If you can find a camera that has a high megapixel number, that's good!  That means you'll be able to print out higher quality pictures and you'll have more room to work w/in your original shot.  (more on that later)
• What if I have to choose between optical zoom and megapixels?  Great question.  I had to do that w/ one of my cameras. I went for the zoom.  I think it's a matter of preference.
  
• Size of the camera.  A camera has to fit comfortably in your hand.  Do you have small hands? Do you have short fingers?  Go to any store that has cameras on display.  Don't be afraid to pick them up and try them out.  Find what feels good in your hands.  Are the buttons in the correct location for easy access, especially the "shutter" button.  A camera has to feel good in your hands.
• Weight of the camera.  I have several different digitals.  One is my DRebel and let me tell you, that's one heavy piece of camera, especially with the longer lenses on it.  Needless to say I use the neck strap.  Some people may like the smaller -- fit in your hand -- type of cameras which also fit easily in your purse or pocket.   It doesn't matter what it is, as long as you're comfortable using it and you want to bring it with you. If it's not comfortable, you won't use it.
• Media cards - A lot of cameras come with a very small media card (compact flash, memorystick, Xd, Sd, etc).  The higher the capacity camera you have (megapixels) the bigger the media card you're going to need.  This is where I say "spend the money on something large."  If you can stand and take shot after shot, w/out worrying about running out of room -- you have one less thing to worry about.  For my Drebel, I have a 4 gig CF card.  The same card also works in a smaller camera I have.  This allows me to take the largest possible pic -- and not worry about running out of room.  Now some older cameras won't take something like that 4 gig card -- and that's ok.  Get what your camera will allow you to use.  It's like having RAM in your computer -- the more you have, the easier things run.
  
• Tripod - not always necessary, but handy to have especially if you have a bit larger/heavier camera or your hands are a bit unsteady.  They have tripods that have "quick release" heads, this means you don't have to sit there and screw things on and off your camera.  Just screw it on once and w/ the flip of a switch it's either attached or unattached from the tripod.  Walmart sells them and they're pretty standard unless you get the least expensive model.  Splurge a little and in the long run you'll save time and frustration.

2) Programs - Not everything is the camera.  Just like with 35mm film, digital film needs to be "developed".  You can work on it, on your computer.  Now all cameras pretty much come with a default graphics program.  I would recommend ignoring it.

• Jasc/Corel Paint Shop Pro - version 9 is the latest & greatest.  Rather than spend $$$ for retail, pop over to eBay and you can grab it for about $35.  Version 8 is fine too and it runs about $20 on eBay.  (These are not illegal copies)
• Photoshop CS -  If you can splurge this much, it's highly recommended. Not so easy to find cheap copies on this.  On eBay it'll run about $300.  I would recommend CS over any of the earlier versions as there's new features that make working with the digital image a lot easier.
• Focus Magic - a plugin for either PaintShop or Photoshop that'll help bring hazy/blurry pictures into sharper clarity w/out compromising the image to the point that other plugins will.
  

I am not affiliated with any of those links or products - just thought I'd throw that in there.

Now that you have everything - the question is.... How?

1. Hold your camera firmly in both hands.  Don't try to do one hand, even if it's a one handed camera (unless it's like a camera phone).  You need the steadiness that both hands offer.
2. Use the eyepiece on the camera.  Sunlight washes out the LCD screen so I've gotten accustomed to just using the eyepiece. 
   
3. Make sure your subject is where you want them to be in the frame.
   
4. Stand with feet shoulder length apart.
5. Breath in - deeply.
6. As you're letting your breath out, slowly depress the shutter button.  Do not press down all the way.  About half way down the shutter will attempt to focus. 
   
7. Until it beeps, do NOT push it down.  It won't take long, only a matter of seconds.   If it doesn't beep, or can't focus -- you're too close to your subject -- too far from your subject.  Readjust the camera and redo steps 5&6.
8. Take more than one picture.  It doesn't take long to take 4 or 5.  Change position and find a different angle.
9. Do not waste time looking at the LCD screen to see if the images turned out while in "shoot mode". You're taking a lot of pictures so even if some suck, there will be 1 or 2 that will turn out fine.

A couple of hints/tips that I use

1. I take lots and lots of pictures.  It's not uncommon for me to go to the zoo for pictures and take about 300.  If only 3 or 4 turn out "spectacular" I'm happy.  Don't be disappointed if every single one isn't a frame able masterpiece.  Most won't be.  From what I've read, not even the professionals are that good ;)
2. Keep the sun low - behind you.  Early morning and evening are considered the "golden hour" for taking pictures.  This keeps the harsh light from beating down on your subject.  Keeps them from squinting.  Natural light is best.
3. Natural light isn't always available.  Play with your flash settings on your camera and see what works for each situation.  Take a few test shots if you know you'll have company over and will be taking pictures later, in the livingroom.  Try and find a place that you can have ample lighting w/out bringing in the worklights from the garage ;)
4. If I have trouble with a specific angle, rather than giving up, I find another angle.  Some simply don't work. 
   
5. practice
6. practice
7. practice

It's only digital.  If it's not good you can delete it.  You don't have to keep it and you've wasted no money on it.  SO very unlike film.  Don't get frustrated.. try and have fun doing it.