When Jesus was preparing for his final moments, he spent an evening with his disciples which we now refer to as "the last supper." During that time with them, he gave a "final discourse" in which he explained quite a lot about how their relationship was going to change after his death and resurrection. Among other things, he promised them that their training would continue (Jn.14-16). Except that from this point on, instead of Jesus in the flesh, it would be the Spirit of God speaking into their lives and teaching them how to live in the new Kingdom.
In his first recorded letter to the Corinthians, Paul describes this process at length, although it appears he struggled to capture this in words. To paraphrase his description:
These things God has revealed to us through the Spirit. No one can comprehend God's ways or how God thinks about things — only God Himself can do that. And we have received His Spirit precisely for the purpose of revealing to us these thoughts of God. But this revelation is not done in clever words or persuasive arguments. Instead our spirit is taught directly by God's Spirit using a spiritual language, that is discerned by our spirit. (1Cor.2:10+)
This is at once both very specific and very unclear! Paul is quite adamant about the nature of this revelation, that it is not something we dream up or figure out through our analytical abilities. God somehow bypasses human language and reveals Himself to us in ways that our redeemed spirit can get glimpses of, if we are paying attention. This is why great Christian leaders throughout history have always spoken of moments when they suddenly realize something they had not seen before, as if their eyes were opened to a new way of perceiving. We sense God's revelations to our spirit primarily as spontaneous thoughts, ideas, and images. The eyes of our heart are opened to new insights and new ways of making sense of the spiritual world, and as a result we are fed in our soul and renewed in our mind. This is how God speaks to us.
In this particular passage, Paul also identifies the type of content God generally reveals. It is noteworthy that Paul does not mention such things as guidance, how to decide which donkey cart to buy, or who to marry. What God primarily reveals to us is God Himself and His gifts of grace to us for life in His Kingdom. Not only because that helps us keep our eyes fixed on Him rather than our circumstances, but also because He is what we really need most of all. Once we have our compass pointed North, we can then find our way much better in our three dimensional world.