Student or Learner
Something tells me I'm into something good.
In this case, does to be into something mean to be in for something?
Ah, memories.....when I was in the third grade Peter Noone (lead singer of Herman's Hermits) was my first true love. In the case of "I'm Into Something Good", "into" means "on the verge of something" or "getting involved with." The singer is saying that he has a very good feeling that this relationship will have a positive outcome.
To be into something means to be interested in it.
"I'm into gardening, motorcycling .."
"He's really not that into you" - He's not that/so interested in you.
As you've probably guessed, the meaning in your example is a little different.