"For both He that sanctifieth and they who are sanctified are all of one: for which cause He is not ashamed to call them brethren." (Hebrews 2:10)
It's when you see and therefore attribute pattern and meaning to randomness and nothing. If you have a far-reaching imagination like me, it shouldn't be hard to come up with an example. This, in lieu of my own apophenic tendencies as I am far too sensitive to share the things I think God is using to speak to me. I don't want to come across as weird or, even worse, schizophrenic. Then again, I believe in God and therefrom, the world is my playground (!).
"Let not your heart be troubled: ye believe in God, believe also in me." (John 14:1)
But! As Jesus alludes to above, we cannot make God in our own image. Nor can we make an image with which we're working in our mind a god. Jesus showed us how to live and so long as we're living and walking in fellowship with Him, it's all good. Apophony, in English, is the slight change in vowel sound so as to shift tense or meaning within a word. It's almost like an outlying effect produced upon words leaving an arbitrary change in its inherent definition. For instance, I could change ran into run but not ron. Because he wouldn't appreciate it. I digress. There are rules for these sorts of things, you know. Perhaps this is why the Tetragrammaton (YHWH) has no vowels? Because God doesn't change. Hmm...
"Every good gift and every perfect gift is from above, and cometh down from the Father of lights, with whom is no variableness, neither shadow of turning." (James 1:17)
So, the prefix apo- means "away from". In the case of the above--another word for a stroke and also slang ("apoplectic") for "extreme anger"--it's literally, the stopping of blood flow from a "part" ("-plex"). I may be waxing all kinds of random here, but the point I'm getting at is this: believing in Jesus truly sets you apart (this is the idea inherent to "sanctification"--being "set apart for God", from the top verse). You may be seen as crazy for integrating all you do into your worldview. Things of another world involving angels and demons and signs and symbols. Strange words and stranger opinions. A world where nothing happens by chance, nothing is random and "all things work together for good to them that love God, to them who are the called according to His purpose." (Romans 8:28)
I believe we can take the minutiae of our day, the little things we notice that no one else does--whether it was God speaking, or not--and tie it in to His glory. Better yet, if you really want to have some fun, ask God to do something for you between you and He. He doesn't disappoint.