Convey your ideas verbally with correct grammar, clear organization, fluid style, and appropriate degrees of emphasis.
Whether communicating in writing or orally, effective communication requires ongoing attention to multiple levels of your presentation, from the level of the sentence all the way up to the level of the presentation as a whole. Communication is ineffective when it violates rules of correct communication and/or veers from widely accepted principles about how to present ideas.
Novice communicators are often more focused on what they are saying than on how they are saying it. They present their ideas in a way that makes sense to them, usually by putting points in the order in which they came to mind. They are good at cataloging or listing their ideas (i.e., "this, that, and the other"). But this "stream of consciousness" or serial ordering may not make sense to readers and audiences, who need to see the logical relationship between ideas (i.e., "this and that, despite the other; therefore, this"). Audiences also typically look for the most important points in particular places, such as the "early" and "late" parts of a paragraph, section, or overall work. Novice communicators ignore such conventions, as well as others governing word choice, grammar, and punctuation, because they are so eager to get their ideas out there. But readers and audiences struggle to get that message because of the many grammatical errors and haphazard choices about structure. Relatedly, communicators who are more focused on what to say than on how to say it may leave their presentations cluttered with typographical errors, "first takes," and too many filler words like "um's" or "also's"---the sorts of things that more competent writers remove through a process of revision and redrafting.
As you gain competence in communication, your writing will be structured so as to highlight and develop a central idea or theme. Key points are stated "early" or "late" in the text and/or its constituent parts, though some of your points may still be "buried" where they are hard to find, and you may still struggle to put your points in logical order instead of in a random sequence. Paragraph breaks, signposts, and navigational words (such as "such as," "however," "nonetheless," "moreover," "next," and "in sum") help to move the reader through the text at a steady pace, pausing to signal emphasis as well as the relationship of the emphasized point to the overall position. You usually convey your points with precise words and fluent sentences that engage the reader's interest, though the length and complexity of some sentences may still interfere with clarity. The amount of emphasis given to different points will be appropriately balanced, though may some points may still be unnecessarily repeated or abbreviated. Your work will show a good grasp of standard writing conventions and grammatical rules, though you may still struggle with one or two recurring grammatical problems. Through revision of your own work, you begin to minimize repetition, locate typos and run-on sentences, and carefully source quotations from or allusions to other authors.
Masterful style means being able to "pull together" all of these skills with minimal coaching or feedback. A masterful writer has internalized these writing conventions so that proofreading errors and unclear passages tend to be very few in submitted assignments. Only a few minor touch-ups would make the text suitable for publication or presentation in an appropriate "real world" venue. When audiences hear or read someone who has mastered the art of effective communication, they have little difficulty grasping the communicator's points and reasoning; whether one glances at the work as a whole, or zooms in to look carefully at the details, it is clear that each word, sentence, paragraph or section has been the result of a deliberate decision in service of a unified goal.
Acknowledgement: I'd like to thank Jenn Borgioli Binis for helpful feedback on an earlier version of this rubric, particularly the wording she suggested for the section related to "novice writing." (And by the way, sharing your own work in draft form can help you become a more effective communicator, too!)