to be into something

[beachboy]

Something tells me I'm into something good.
In this case, does to be into something mean to be in for something?

[bhaisahab]

Something tells me I'm into something good.
In this case, does to be into something mean to be in for something?

It might, but it might mean involved in something good. You'd have to ask the songwriter what he meant.

[Ouisch]

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.

[Raymott]

Something tells me I'm into something good.
In this case, does to be into something mean to be in for something?

You've been answered adequately by the others. But since your title is descriptive of a common idiom, I'll give its other more common meaning.
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.