"What is the best way to prune a tree?"

That depends a lot on the tree and why you are pruning it. We will need more specifics and maybe even a picture to give you specific advice on your particular situation.

"Is there anything specific I should be looking for?"

There sure is!

Many useful guides are available on line. Here are some:

US Forest Service on How to Prune Trees

ISA on Pruning Young Trees

ISA on Pruning Mature Trees

And, of course, you can find many many many more with a quick google search. You can also find many threads, in this forum, on the topic. Narrowing down your question will help us provide more specific info.

first you ID the plant.. whether it is a tree.. a shrub.. or a conifer.. as there are slightly different rules for each type ... and sometimes peeps confuse them all ...

we can usually do that here.. with a pic of the whole ... a leaf and the trunk ...

and while you are waiting for the ID.. you can peruse brandons suggesting reading ...

and then.. with the pics.. we can make suggestions as to a favored shape.. etc .... and if we really like you.. someone might even photoshop a good plan ... WELCOME TO GW ...

a good pruning saw is also a good investment .. if you have a lot of pruning to do ...

more info please

ken