Memorize the note names. This is the first step to reading notes quickly. There should be no gap between seeing the note and saying the name.
Connect the notes in your head to the notes on your instrument. You can mentally practice by picturing yourself playing a song. Look at a page of sheet music and think about how your fingers would move when you played each note.
Forge this connection on the actual instrument. The notes should mean something to you, but don't think about the name of the note before you play it. Eventually you will automatically see a note on paper and connect it to a note on your instrument.
Practice. No matter how smart a musician is, nothing substitutes for practice when it comes to reading music. It is important to balance repetition of songs you can already read with songs you haven't seen before, called sight reading.
Fill in the names of notes on pieces of sheet music. Do this as quickly as you can without making mistakes. This is a good type of practice when you don’t have an instrument with you.
Read pieces of music that get progressively more difficult. Pieces with shorter note values will challenge you more until you can read music perfectly.