I don't know how to explain this well in words, but there's at least two different methods for flipping stuff in a pan, because you have either curved or straight sides on the pan. I personally find it easier to do in a curved sided pan:
I extend my arm forward, then quickly flip the back of the pan up while pulling back at the same time. The curved side basically acts as a ramp to propel the food up and over.
For a saute pan (straight sides), follow the technique that ElendilTheTall explained, where you tip it first.
A few things to remember when trying to flip your food : if the food's stuck to the bottom, it's not going to flip. Give the pan a quick shake first, to see if you need to stir to loosen any stuck bits.
And for the practicing -- besides just practicing with dry things first ... I'd suggest you start with just a little bit, get used to it, then add more ... and add more of something else, as with more than one color in the pan, you can see how well you're distributing things when you flip. (eg, lentils, other beans, rice, dry pasta, etc.)
Start with a mid-sized pan, as larger pans are actually more forgiving when catching, but too large makes it heavy and difficult to get a good flip. (ie, don't start with your cast iron).
If you have a grill, or a table outside to practice on, the cleanup's even easier. (although, use a cold grill, just for practice). You can also practice with just water, if you're outside, without as much worry.
As for when to do it -- lots of small things; stirring risks keeping the bottom bits on the bottom, and the top things up top, so things cook unevenly. Even if you use a spatula to flip, like you might for a larger item, the middle stuff stays in the middle.
The other advantage is that it only takes one hand -- I generally keep my right hand clean when cooking, and stirring sometimes takes two hands -- one to keep the pan still, while the other one stirs. It's also quicker to get a more thorough mix than stirring.