What are some of the main tenets of Radical Empiricism in William James's essay "A World of Pure Experience"?
Let me preface my answer by saying that the list of main tenets of Radical Empiricism are different than the list of main tenets from the actual essay you mention: "A World of Pure Experience." Let me explore the main tenets of the latter first, just in case that is needed as well.
In "A World of Pure Experience," William James nicely arranges his essay into a few main tenets. They are as follows: Radical Empiricism, Conjunctive Relations, The Cognitive Relation, Substitution, and Objective Reference. This being said, Radical Empiricism is only the first of these ideas but, yes, it in itself is worthy of being explored further. If you would like to read the full text, I have included a scholarly link for you.
Thus, let's take James' first idea that you ask about. First, let's relate that James' rejects the idea of subjectivism (that the moral idea of something being good or bad is the only thing that is important). No, James believes in his self-coined concept of Radical Empiricism which is simply an extreme form of empiricism. James asserts that experience that leads from consciousness is the main idea. However, experience in itself is not enough, one must embrace experience. This takes consciousness to a new level.
William James' actual description of Radical Empiricism is as follows:
Empiricism, on the contrary, lays the explanatory stress upon the part, the element, the individual, and treats the whole as a collection and the universal as an abstraction. My description of things, accordingly, starts with the parts and makes of the whole a being of the second order. It is essentially a mosaic philosophy, a philosophy of plural facts, ... But it differs from the Human type of empiricism in one particular which makes me add the epithet radical.
This hits the nail on the head in regards to James' definition. He rejects rationalism and subjectivism and goes beyond simple empiricism because he needs to go further than Human Empiricism. James' even goes further with this philosophy in describing his "radical" addition to the phrase:
realas anything else in the system.
For such a philosophy, the relations that connect experiences must themselves be experienced relations, and any kind of relation experienced must be accounted as real as anything else in the system.
Even relations, then, according to James, must be experienced. Further, it must be accounted for as "real." This expands his idea of consciousness.