English Standard Version (ESV)
Spend enough time around people, and you can get a sense of what their primary motivation is. Some people are easier to read than others, but you can eventually determine what drives people by studying their words and actions.
Here, one gets the sense that Cornelius and Peter are guided by the Holy Spirit. The way they talk -- there is a strong connection between their lives of prayer and their next steps. These are men who invest heavily in their prayer lives, and then they follow up on what is revealed to them. They expect God to guide them, and when God gives direction, they obey, even when it's unclear where this will lead.
Now, our prayer lives are probably different. We may not hear from the Holy Spirit in the same way Peter and Cornelius seem to. But wouldn't it be wise to invest the same energy and time into our prayer lives, with the expectation that God will lead us? I don't know what would happen next, but I imagine it would bear fruit that would draw us closer to God.