So, if you're facing down the pruning sheers and you're terrified, we're here to hold your hand. And if the worst happens, remember that plants are a lot like hair: mistakes grow out, okay?
Another type of cut, known as heading, is a great deal like pinching, except that you cut further back along the branch. That's not so scary, is it? To head a branch, you cut right above a leaf to stimulate dense growth below the cut.
There's also shearing, which is pretty much exactly what it sounds like. If you have hedges or shaped shrubs, you need to shear them to keep them in shape. This just involves using clippers to cut along an angle to shape a squared hedge, topiary, or other desired shape, and it works best with small-leaved plants. (If you try to turn something with big leaves into a hedge, shearing will look clunky, because it cuts right through leaves and branches indiscriminately.)
So, now that you know the basics, what do you do when you have a tree in front of you?
First, assess it. Walk all the way around. Look for diseased or dying branches. Take note of branches that cross or tangle with each other and look for areas of overgrowth as well. Consider whether you like the way the tree or shrub looks -- is it bulky and shapeless? Is it lopsided?
As a general rule of thumb, you never want to prune more than 1/3 of a plant's growth, although some trees and shrubs like harder pruning. Things that grow quickly and aggressively (like holly) tend to respond to aggressive pruning more readily than those that grow slowly.
Start by removing obviously sick branches along with growth that's crossing or tangling, because that's going to cause health problems for the tree. The kind of cut you should make depends on whether you want to simply thin growth or head, promoting more growth below the cut -- think about how this will affect the shape of the tree. Next, you can start to assess areas of the tree that need attention: does a tree have a thick canopy? This could block light and make it hard to thrive, so you need some thinning cuts.
Aesthetically, trim trees that have uneven growth or other issues, heading and thinning as appropriate. Something you may also want to consider is the use of thinning to create a tree-like growth habit for shrubs that could go either way; this will make it easier to maintain them, and they may look more attractive.