There are lots of books available on textual criticism, many extremely technical.
My favorite is Neil R. Lightfoot’s How We Got the Bible. My copy bears a 1962 copyright date, and it was a textbook in a Bible class at my church when I was a teenager. It was part of the old The Living Word Bible class series from Sweet.
Fortunately, it’s not just still in print, it’s been updated as of 2003. Readable, expanded to 225 pages. You should own this book.
If you know a little Greek, then you can make use of a critical apparatus, such as Novum Testamentum Graece: Nestle-Aland (Greek Edition), probably the most popular apparatus. The editors’ opinion of the likely Greek text appears, with very extensive footnotes giving all the variants and the manuscripts supporting each. An English introduction explains how to interpret the abbreviations and codes.
However, if like me, you’re not a very good Greek reader, you might prefer the same thing but with interlinear English added: ESV Greek-English New Testament: Nestle-Aland 28th Edition and English Standard Version (Cloth over Board). Bring one of these to Bible class, and you’ll win every argument by sheer intimidation!
You may be a little offended at this, but I’ve been very impressed with the Wikipedia’s materials on textual criticism. Your high school or college teachers may not approve, but someone put together better materials here than you’ll find in a lot of books.
My son who is working on his Chemical Engineering doctorate, tells me that many graduate school professors have their students write Wikipedia articles in their fields, resulting in some top notch resources.
For example, you can Google “Manuscript P47” and land on an article that tells you all about that papyrus. Links take you to the collection it’s a part of, the library where it’s found, and the author shares that the manuscript gives “666” as the number of the beast rather than “616” as in Papyrus 115 (a 3rd Century fragment).
I had to check my library to make sure I still had my copy of “How We Got the Bible.” Mine carries a 1963 copyright. I took one class from Dr Lightfoot at ACC in 1968 or 69. Nice to hear his work has “stood the test of time.”
How We Got the Bible by Neil Lightfoot is also one of the books published by Eastern European Mission in several of the 20 languages of the old Soviet Union bloc of nations.
Wikipedia is a generally good source. It is much improved over its earlier, justly criticized, content.