You hear a song you like.
You can pick out the melody line using your right hand.
You don’t know what chords to play on the right hand.
Usually, if you know it, you’ll know the whole sequence of chords to play. If you don’t know, you’ll be picking the chords by trial-and-error, right?
What you need to know now, is you need to be familiar with many chord progressions. You need to know the songs that use those progressions.
For example, many theme songs from Japanese animation as well as live dramas use the progression IV-V-iii-vi. That’s 4-5-3-6 of the major scale. You can play Yui’s Rolling Star, or TM Revolution’s Heart of Sword, and so many more.
The key is to know the chord progressions for a few songs, and you will have it wired inside your head already. You will be delighted and surprised to find those progressions readily identifiable in subsequent songs that you happen to listen to, and immediately, you will be able to play on the piano!
Another chord progression is the minor progression I-III-VII-IV, or 1-3-7-4. It’s the minor scale, take note. Songs which use this include Boulevard of Broken Dreams by Green Day, What Goes Around… Comes Around by Justin Timberlake, and Wonderwall from Oasis. Play the progression on the piano first, then include the right hand melody while your left hand plays the chords.
After playing a few times around different keys, with different songs, you will be used to the chord progression, and subsequently, able to recognize it in songs.
The more progressions you know, the better.
The more familiar you are with all 12 keys, the better.
The more familiar you are with all kinds of chords, the better.
The key is to keep playing.