Arcing and tracing are great ways to analyze the flow of an argument in a passage, especially discourse (such as the epistles; it is more difficult to use for narratives). John Piper has found it helpful. I know of several who say it revolutionized their Bible study. Thanks to help from Dr. Brian Vickers (SBTS), Dr. Jim Hamilton (SWBTS), Matthew Wireman (Ph.D. student at SBTS), and my friend John Beeler, I have been learning this and hope to share it with others. Here are some online resources to help you learn about and use this excellent method, which is well worth the time and effort it takes to begin to learn.
Note: Arcing and Tracing have the same goal. Arcing uses curves (arcs) whereas tracing uses brackets (usually easier to read). One can easily translate an arc diagram into a traced one or vice versa, depending on one's preferences. Arcing in the Piper booklet below is presented as on a horizontal plane, utilizing only verse/proposition numbers without the text. The method on the BibleArc website uses text and arcs it vertically. Tracing uses the text with brackets instead of curves. Now that I've confused you, be sure to check out the resources below for clarification.
• www.BibleArc.com has to be one of the most innovative and helpful websites I've seen. It allows you to arc a passage of Scripture, save as a .pdf, and share with others. It has all the tools for dividing the verses into propositions and labeling them with their relationships to each other. It even allows you to save your own arcs on the web at the site to go back and edit or download again. (HT: Matthew Wireman)
• For more on "arcing," see John Piper, Biblical Exegesis: Discovering the Meaning of Scriptural Texts (Minneapolis, MN: Desiring God Ministries, 1999), 48pp. booklet with chart. Order from www.desiringGod.org at <http://www.desiringgod.org/Store/Booklets/ByTopic/54/85_Biblical_Exegesis/> or download for free at <http://www.desiringgod.org/media/pdf/booklets/BTBX.pdf> (booklet only; chart not included in online version).
• For more on "arcing" and "tracing," see Thomas R. Schreiner, Interpreting the Pauline Epistles (Grand Rapids, MI: Baker, 1990), 77-126. These two chapters are available online for free from links at his faculty webpage <http://www.sbts.edu/Academics/Faculty/Theology/Thomas_Schreiner.aspx>:
"Diagramming and Conducting a Grammatical Analysis," in Interpreting the Pauline Epistles (Grand Rapids: Baker, 1990), 77-96. Non-exclusive, one-time permission is granted to use this chapter, excluding any permission of a third source. The permission applies to this usage only. Baker Academic, a division of Baker Publishing Group, copyright 1990. <http://www.sbts.edu/docs/tschreiner/book_IPE_chapter5.pdf>
"Tracing the Argument," in Interpreting the Pauline Epistles (Grand Rapids: Baker, 1990), 97-126. Non-exclusive, one-time permission is granted to use this chapter, excluding any permission of a third source. The permission applies to this usage only. Baker Academic, a division of Baker Publishing Group, copyright 1990. <http://www.sbts.edu/docs/tschreiner/book_IPE_chapter6.pdf>
Here are some additional tips to make use of these methods.
1. Pray. Ask the Lord to open your eyes to see Him in His Word (cf. Ps. 119:18).
2. Choose a literal translation. The New American Standard is probably the best choice for its accurate rendering of prepositions. (Other options: ESV, NKJV)
3. Choose a passage. Try to find a unit in the length of a paragraph. Start with shorter units while learning tracing.
4. Divide the verses into propositions.
5. Read the passage and highlight key words that will serve as indicators of the relationships between propositions.
6. Find the relationships within each verse itself first. Then find relationships with neighboring verses. Then begin to link to other verses/relationships in the text.
7. Use your findings to structure the passage (outline it).
8. Summarize the argument of the passage and identify the exegetical idea/main point.
9. Now you are ready to do further study (observing repeated/contrasted words and concepts, looking up meanings of individual words, noting the verbs, relating the passage to the rest of the book and the whole Bible, finding application, etc.).
Note: If you are a serious student, I would be glad to share another resource or two with you that I have permission to share via email, but not to post on the web. Please email me with "arcing/tracing helps" in the subject line if you need further help.