Basically, blur photos are caused by either by out of focus or by camera shake.
Camera shake is caused when we are not able to hand hold the camera while we are capturing the photo causing blurred photos.
Back in the days of 35mm (which I started with) you don't have unlimited digital images to capture. You are limited by 36 shots... of which you are not even sure how it will turn out till you develop it 2 days later.
So every shot... must count. You cannot afford to make simple mistakes like camera shakes... period
To the most of us, we use the Reciprocal Rule, which minimizes camera shakes.
The Reciprocal Rule states that you can safely handhold the camera if your shutter speed is faster than the reciprocal of your effective focal length
Example:
Focal length is 120mm* equiv: Shutter speed should be faster than 1/125s
Focal length is 28mm* equiv: Shutter speed should be faster than 1/30s
As you can see, the longer the focal length, the faster you will need the shutter speed to be.
*Please note that I have written the focal length in the equivalent length because, most digital camera come with a crop factor of 1.6 times. Meaning you have to take whatever focal length you have and times it with 1.6. I will explain more about the crop factor next time.
By following the simple rule, you'll be able to minimise your mistakes. Of course as you get better with photography, you'll know what is the slowest speed that you could hand hold at.
I personally was able to hand hold at 1/5s at 105mm with IS. That was probably a lucky shot, but it is not impossible. With your digital camera, you could just practise and practise.
Most of the new Canon Lens comes with the Image Stabilizer (IS) feature which will greatly help with camera shakes. It will allow you to hand hold up to 3 stops slower.

Shutter Speed: 1/13s
Aperture: f5.6
ISO: 1600
Focal Length: 114mm equiv
IS Mode: ON

Shutter Speed: 3.2s
Aperture: f32
ISO: 1600
Focal Length: 114mm equiv
Lens IS Mode: ON

Shutter Speed: 1s
Aperture: f18
ISO: 1600
Focal Length: 127mm