Pruning is an art form. It is vaguely akin to Bonsai, in some ways, but on a grand scale.
Absolutely everyone does it differently even if any two people have identical goals as their outcome. So don't feel like you have to attain some sort of perfection when you do this. That said, you can easily ruin a tree forever if you do it wrong. Comfortable? OK, let's dive right in.
Depending upon what kind of tree or bush you have, your plant will need different care in every way including pruning. Blueberry bushes can get by with no pruning or just taking out any dead wood. Alder trees need be pruned only to your taste as to what you want them to look like or the more practical aspect of whether you can get under them easily enough to harvest the raspberries you put there. Apple trees...well, there are different approaches. There is some new research out of Cornell University that shows an unpruned apple tree may produce a bigger crop than a pruned apple tree. Masanobu Fukuoka of Japan came up with this idea during the middle of the last century so it is nothing new. But the "quality" of the apple can be changed by judicious pruning. So many choices, so few trees to test them on.
Pruning of apples can be done to strengthen the tree structure, make it easier to get inside to pick, keep it short enough to pick without using a ladder, be able to walk/work under it easily, make it look like a weeping willow to fit your yard motif, etc. Everyone needs or wants something different from their trees.
Making the pruning cut angled or flat. Used to be an angled cut was all the rage now it has been shown that a flat cut is better for the tree. It makes sense as less inner tree branch open to the air and microbes is best. If you are removing anything larger than what a one hand pruner can manage, you must first make a cut on the underside of the branch opposite where you anticipate the main cut to end. Without doing this, you can strip the bark for a long way and expose the tree to infection. Losing a tree this way is sooo wrong.
There is weak branching and strong branching. The weak ones can split a tree down the middle, if left as one of the main "scaffold" branches when the tree is young. This is a critical item to become familiar with and easily avoided. Weak scaffold branches are sharply "V" shaped and must either be changed, if caught early, or strengthened, if caught late. Early catching means you just cut one of the branches off and work from there with the other as the main support branch. Late catching means you have to provide lateral supports via grafting which is far more difficult. Go with the first option although the second is fun to do and rarely seen today. The only place I have ever seen it, beside in my yard, and where I got the idea is in a hundred and thirty year old abandoned apple orchard in the hills above Corralitos, CA. They had made three main scaffold branches in a "vase" pruning style coming off the trunk and each of the branches was grafted to the other about a foot and a half above the confluence with the trunk to form a triangle horizontal to the ground connecting the branches. It was beautiful. All the trees had it.
The trick to successful pruning is to be able to visualize how the tree will look in five years due to your pruning. You need to know how the tree will grow as it matures so you must be able to look at pictures of the growth pattern of your variety of tree and how others have manipulated it. Get online or to the library and look it up or visit an orchard and study the pruning marks and growth pattern. All fruit tree varieties are slightly to completely different in growth patterns. The devil is in the details and you will live with the outcome of your understanding of the details for years to come so spend some time with this aspect of growing fruit. Everyone that passes will see what you have done and how well you understood what you did. Spend some time on planning your pruning. Sit with the tree and visualize where you want it to be in five years and where you may need to make the cuts to get it there. There's no rush. You can always do it next year or later in the summer. It is easiest to do when all the leaves are on the ground. Keep in mind, it is a bit difficult to watch the knowing look of a thoughtful pruner obviously trying not to say anything about your tree other than, "Oh my, um...what a...nice tree".
Hiring a pruner can be problematic unless that pruner comes highly recommended and even then I would want to see examples of their work. I have seen ruined trees that the customers thought were done quite well and would happily recommend the pruner to others.