Compare playing a piece to telling a story:
The notes correspond to the letters.
The phrases correspond to words and sentences.
Phrasing and articulation correspond to the intonation.
Therefore, you must have a story to tell, and the intonation must fit the character of the story.
Begin with figuring out or making up your own mind what the piece is all about. Do certain sections depict happyness, sadness, rage, etc.?
Once you have done that, play around with different ways to achieve the corresponding sound. Try staccato, portato, legato, rubato, all the "atos" you can think of. Play with crescendos, decrescendos, accelerandos, all the "ndos" you can think of. Put accents on the first note, the last note, the second to last not, every other note, etc.
Of course, there are certain "rules" for articulation that depend on the piece, the composer or the period the piece is from. But those rules are only guidelines. Don't get trapped by them.
Listen to different recordings of the same piece. Analyze where they differ. How do they differ? What is the resulting mood or feeling. Do you agree with this rendition, or would you play it differently. If so, how? Sing the piece the way you would like to play it. Then try to reproduce that sound on the piano.
You may not know how to achieve a certain sound or mood through articulation, yet. So, the next time you go to your teacher, tell him/her "I think this section depicts happiness, but it is immediately followed by deep uncertainty and a dialog between two opposing characters. How do I bring all this out". You'd be delighted how much fun this aspect of music is. And you will end up a good storyteller, which is what music is all about.