The thing with the invisible is that well ... it's not obvious, at least not if you don't have special "eyes". In this “Invisible x Visible” dichotomy, the dependence on the senses and on the practical life makes the “visible” side weigh more strongly, generally. So, how to separate an apparently mundane phenomenon from a “sacred” or “touched by the invisible” one (which we will take here as synonyms)?
People has long been defined by the clash “Visible x Invisible” and “Sacred x Profane”. Great minds have thought about this question thoroughly and entire societies have dedicated their own lifestyle to, for example, erasing this duality. For the contemporary Western person, the invisible seems to be more and more restricted: either on the church on Sundays or on fairy tales. However, it is clear that in practice those things are intertwined, as stickers on cars point out, such as “It was God who gave it to me” or “Chance does not exist”. Secularism has not worked as well as you think.
Fact is: even if you understood that everything in your life is a communication from the invisible (as a saint or an enlightened one might do) simply ignoring that certain things are just randomness caused by the matrix of existence would probably not be very wise. After all, everything can move someone to divinity, but not everything needs to be a direct manifestation of that.
What would characterize a situation of direct invisible manifestation? Tough one. A number of symbols and meanings need to be analyzed. Things that are likely to only make sense in a very specific context should be considered. I could not and would not dare to give examples or try to suggest to anyone how exactly this should be done. However, this short text brings a suggestion of exercise, which is: use five minutes of your day to recognize what is sacred / magical / invisible in your life, how it has been presented and how you have brought it into your reality.
It is not wise to dedicate ourselves to a path or to a faith and not to worry about how it talks to us. Do this simple exercise and write down your impressions. Sometime later, review everything you've produced and put it in your current perspective. The result will sure be interesting and important.