"How was your day?"
"Y-y-you t-t-too"
^^
OP, you're overthinking it, most people are literally trying to pass a pleasantry.
Its fairly easy to start the conversation, just throw it back at them.
Person: How are you?
You? Fine thanks, days going grand. Yourself?
If they just go fine or something that you cannot latch onto, it was just a pleasantry. (not masturbating or shivering with fright helps keep the conversation going).
If they go "yeah, great, nice weather helps, or "not bad, long day though" or something similar, then you've got an opening.
Truthfully, its about listening to people. I used to be terrible at such things, until one day I realised that I simply wasn't listening to people, I was just too busy saying about MY day or whatever.
Listen to people and respond.
(I still don't care what people say but I'm better at faking it.

)