Without deep academic explanation the main reliable principles of an exegesis that are important in understanding the Scriptures is first a literal simple reading as an interpretation of the text, unless the text indicates simile, parable and metaphor and secondly context.
Exegesis comes from the Greek word meaning to 'lead out' a fundamental explanation and interpretation of primarily a religious text. 'Biblical exegesis' is the correct term used for identifying and correctly interpreting Bible passages.
Exegesis includes a broad collection of critical disciplines including:
Textual criticism - the investigation into the history and origins of the text, historiographical criticism - the study of the historical and cultural backgrounds for the author, the text, and the original audience and other areas like literary genre and grammatical and syntactical features in the text.
A personal Bible study type exegesis simply includes the following:
Introduction:
1) Aim and objective
Main chapter:
3) Text selection
4) Exploration of orthodox Bible commentaries, which might include topics like historical context, social and or economic structures of the time. It will certainly contain cross referencing.
5) Theology and Application
Conclusion (Draw from above)
Bibliography (Some reliable referencing)
An academic exegesis might include the following explorations:
Introduction:
1) Statement of investigation
2) Aim and objective
Main chapter:
3) Greek to English translation
4) Historical Context
5) Literary Structure and Grammatical Study
6) Theology and Application
Conclusion (Draw from above)
Bibliography (Extensive referencing)