First, it is important to distinguish between two very famous pieces that share a similar title, as this affects which sheet music you need.

If you are playing the instrumental version, pretend you are singing the lyrics. In measure 12, "So close your eyes..." your right-hand finger should lean into the key slightly. Use finger legato (holding one key while playing the next) rather than relying purely on pedal.

Most published versions are "Piano/Vocal/Chords," meaning the melody is in the right hand with lyrics printed below. You can simply ignore the lyrics. Pure "Piano Solo" arrangements are rare for this specific title, but the vocal version works perfectly as a solo.