From a modern hermeneutics perspective:
First, the distinction needs to be made as to whether or not you're asking when or how. When indicates a circumstantial acknowledgement of the purview of Scripture on one's life whereas how indicates constant purview of Scripture.
There are also three words that seem to be used interchangeably but that are actually quite distinct: meaning, significance, and application. These words move from objectivity to subjectivity along a spectrum, respectively. Thus, meaning is the most objective and application the most subjective. The goal of this approach is to start with finding the object meaning of the passage, understand its significance to the original audience and find contemporary parallels, and then to apply that significance (the "nugget of truth") to your life and the life of your community (of faith or otherwise).
A common approach would be to follow a process such as the following:
- Place the passage in literary context.
Immediate context (how does the passage fit into the story)
Larger Context (how does the story fit into the larger narrative)
- Place the passage in cultural/historical context.
- Identify significant questions arising from the passage and/or its context.
- Identify keywords that may need exploration.
- Synthesize this information into a picture of how the original audience would have received it.
- Why would this be important to the original audience (immediate truth)? *
- What about this is timeless (contemporary truth)? *
- How is it possible for me to express this timeless truth in my life? Also, how does this timeless truth impress itself upon me/change me? *
This is just a rough outline, and is a from-memory summary of Klein, Blomberg, and Hubbard's Introduction to Biblical Interpretation. More advanced studies should expand steps 1-5 by using many different types of critical methods (socio-rhetorical criticism, sensus plenior, source criticism, text criticism, historical-grammatical etc. which are not, in and of themselves "schools" of hermeneutics, but methods to be applied by exegetes who are following the "hermeneutical process.") which expands the scope of potential meanings.
So how do you know if/when a passage "applies" to you? It depends on your intent and process. If you are responsible with the text, then the application will become evident.
*[Note that steps 6-8 are more subjective and it is at this point that theological and doctrinal frameworks begin to come into play (and this is acceptable for the purpose of seeking application from a text).]