Do a course/workshop/lesson

When I started out I took a six week short course for two hours a week. It was great. I would never have read the manual, I do now, to learn the basics and master the jargon. Learning the basic from someone who knows allows you to get into the fun, creative side of photography and not worry too much about the technical side.
Bowman Photo Workshop : Getting Off Auto

Study

Read, watch, browse and listen. The internet has so many great sites to learn photography. I spent a fortune on photography magazines and book.
I'd recommend books by Michael Freeman, Tom Ang, David duChemin and Joe McNally.

Copy

Study the "masters", then try to copy them.
Where is the light (sun/flash) coming from? What do you like about their photos? What angle are the photos taken from? Do they use a certain aperture?
Here's a link to a few great photographers who have inspired me.

Get Close

"It your photos aren't good enough you're not close enough"
Use your feet NOT your zoom. Get as close as you can to start with and then move back.

Rule of thirds

Try having your subject off center. Divide the frame in thirds vertical or horizontal and try putting your subject on the thirds

What am I looking at?

Before you press the shutter ask what's the subject of your photo? What do you want the viewer to look at?
If you don't know how is the viewer supposed to?

Ask

Contact your favourite photographers and ask for their advice. How do they shoot, or better how did they get a certain image? You'll be surprised how many photographers share their "secrets".

Learn to edit

Editing your images is about 1/3 of photography in my opinion.
Learn to use Lightroom, Photoshop, Aperture or Picasa, and your images will look MUCH better. YouTube is a great site to learn about editing photos.

KISS

Keep It Simple Stupid. Remove everything from the frame that could be distracting to the viewer by changing your distance, angle or aperture.