Route 66 was written by Bob Troupe and performed the first time on an album by the same name by the Nat King Cole trio released in 1946. Below is a video of the trio playing, originally in the key of G. Most people play or sing this in F, but I went ahead and kept it in G for educational purposes.
This website his several resources for you on how to play this tune.
First and foremost, I encourage you to learn the melody from the recording. You can use a real book, but sometimes the chords are wrong, so I advise to use the recording first.
Once you’ve learned the melody and play along, I would advise you to start learning the chords.
After learning the chords, I would advise to learn the two note voicings for piano proficiency and for use as guidetones. I would also recommend practicing a bass line, which you can play while others are soloing if you are in an educational setting.
Once you have internalized the chords and you can play the bass line, practice the two note voicings on the piano with the recording. Listen to the pianists comping for ideas about rhythm.
Hope this is helpful!