In 2008, Colin Smith posted a 13-part series as an introduction to textual criticism. I thought that this would be an ideal time to create a post with links to all of those in the series. Hopefully this is edifying and helpful to you!
An Introduction to Textual Criticism: Part 1–Introduction
An Introduction to Textual Criticism: Part 2–The Writing and Transmission of Ancient Documents
An Introduction to Textual Criticism: Part 3–Textual Errors
An Introduction to Textual Criticism: Part 4–The Role of Church History in Textual Criticism
An Introduction to Textual Criticism: Part 5–The Received Text
An Introduction to Textual Criticism: Part 6–The Challenge to the Received Text
An Introduction to Textual Criticism: Part 7–The Task of Textual Criticism: Weighing the Evidence
An Introduction to Textual Criticism: Part 9–“Traditional Text” Positions: The Ecclesiastical Text
An Introduction to Textual Criticism: Part 10–“Traditional Text” Positions: Byzantine-Priority
An Introduction to Textual Criticism: Part 12–The Eclectic Text Position: “Reasoned Eclecticism”
An Introduction to Textual Criticism: Part 13–Concluding Thoughts