Frank Rose, who has published excellent books on the plants of the Santa Catalina Mountains north of Tucson tells me that he never keys out plants. He either gets introduced to the plant by someone who already knows it (the best way), or takes a specimen to someone who is able to identify it, probably a botanist at the herbarium.
The next thing you will need is some kind of book that explains the extensive jargon used to describe plants. By and large, learning to key out plants is all about mastering this jargon. Although it is intimidating, and apparently endless, it does have an end and is both concise and precise. Experience is all important. You learn to key out plants by keying out plants. You can learn the book definition of pilose and tomentose, but what you really need is to be able to recognize it when you see it on a plant.
Using the keys ought to be simplicity itself. You start someplace and then start answering questions that take you to one of two choices. You repeat this until you arrive at your plant. Someone with experience can do this rapidly. The beginner will need to look up each term and wonder about what it means.
It is a huge help getting started if you can look at the plant and either know or make a good guess as to the family it belongs to. If you know that it is a Brassicaceae, you go into your flora and find that family and start running the keys. If you don't know the family, things will be more difficult. There is usually a family key at the start of the flora, but these can be tricky.
A first concern is the ecological damage you may do by collecting a plant. If it is rare, just don't. If it is all over the hillside, taking a stem or even an individual is unlikely to do any real harm. If there is only a small local colony or just one individual, I would be reluctant to collect anything.
The next issue is getting it home in a condition that allows it to be studied. Zip lock bags are the answer, sometimes with a bit of moistened paper towel in this desert climate. A small ice chest in the vehicle with a frozen gatoraide bottle of water to keep things cool can be a big help on the drive home. You will probably want to study the plant either the same or next day. Beyond that, you are into pressing plants for preservation, which is not something I will talk about here. Pressing plants changes many characteristics, and working with pressed and dried specimens adds another layer of complication beyond working with fresh plants. If you get really serious, there will be a time for that.
I am in Arizona, and the "Arizona Flora" does not have nice plant descriptions or drawings. I suppose this is good in a way, otherwise the book would be bigger than it already is. What you can do is to find your plant and then study the keys "in reverse". Find out what characteristics the key uses to distinguish your plant from its brothers and sisters.
Tom's Plant pages / tom@mmto.org