I do think what @Garrett Linney says is true, that God speaks in what He has already spoken. Sometimes it's really hard to figure out what that is though, or how it translates into our lives. My experience growing up was that these verses were invoked all the time, but nobody would translate that into "ok so here's how we can use Scripture to discern righteous actions that align us with God's thinking and desires for us." So even though I think 2 Timothy and Hebrews are good guides, we still have the problem of trying to discern how to see Scripture as "profitable for teaching, for reproof, for correction, and for righteous training..." Knowing that Scripture is a guide is much different than knowing how to use Scripture as a guide.
I do think there are plenty of tools to help discern how to use Scripture as a guide. The one that has been the most freeing and directing for me though has been measuring my own ways/actions/thoughts by how God characterizes and names Himself. We are all image bearers of God, so righteous action will reflect God's character. When I'm trying to discern speech, actions, or even beliefs, I can ask myself a few questions to see 1) if I'm in line with God's character and 2) if I'm bearing His image well. Questions like:
Does this speech/action affirm God's Names and character, for myself and/or others? (for discerning speech/actions)
Do my speech/actions draw people closer to experiencing/seeing/hearing God's Names or character? (for speech/actions)
How can I better realize God's character in my own life and reflect it better to others? (for speech/actions)
Have I believed anything that's counter to the Names or character of God? (for discerning beliefs)
Have I ever ascribed something to God that is contrary to His Names or character? (for beliefs)
When I'm experiencing situations that are contrary to God's Names or character, do I recall and call upon the Names of God? (for actions? Or prayer maybe?)
I'd love to hear others' thoughts and reactions to this as well :)