Plant Identification

My approach to identifying an unknown plant is

If the plant is on your property take a specimen of mature foliage, this may be tricky if the leaves are way up above you, look on the ground for fallen leaves. If it has flowers gather one or two, these will make your task much easier. Be careful if the plant is young, perhaps only take photos.
If it is not on your property, take photos of leaves, front and back, branches, trunk and flowers.
Get your own copy of a book with a plant identification key in it, perhaps start out by borrowing one from a library. Have a look in bookshops for one you might like to buy for yourself. While they are all doing the same task they approach it with slightly different outlooks.
Maybe get one or two plant picture books that cover the area you live in, that applies to books with identification keys as well. My book collection only covers rainforest plants of eastern Australia, some only cover the state of New South Wales.
If you are lucky the plant will be quite distinctive, often enough you will have to try and split hairs, pay attention to the details in print, look at the photos, look for distinctive features.
Remember, plants don't read books.
Find someone who knows more than you do and ask them.

Of course you could start out this way if you only ever want to identify one or two plants but in the long run it is more satisfying to do it yourself if you have a few to do a few.