When you feel you’ve begun to get the song under your fingers, see what connections you can find between the main bits of the tune and the patterns of the note-dots on the chart. Feel the pulse of say 4, beats to each ‘bar’. See if you can connect dot-clusters with phrases in the tune. Scribble over the chart in pencil and make it a working document; assign ‘note pitches’ to the dots using the pattern EGBDF for the staff lines moving up, and the pattern FACE for the spaces moving up, with '#' (sharp) signs raising a note half a tone and 'b' (flat) signs lowering it. Don’t worry about the precise note durations and rests, they’ll fall into place as you feel the groove of a song.
Trying to read a score and play a tune against a soundtrack has the problem that you can lose your place if you make a mistake but the track carries on, whereas if you’re reading a story, you can take all the time in the world, (to quote Louis Armstrong!) So if you trip up or get lost, just go back to the beginning and give it another go.
If the chart doesn’t make the process easier at this stage, ignore it. Music is for hearing and listening to, while notation is for reading; the two are not the same and require different treatment. In my view, it’s more important in jazz to respond to what you hear than what you read; jazz inflections and subtleties can’t always be represented in notation and a lot of jazz is never transcribed or written down. Musicians all over the world, and going way back in time, play(ed) without writing anything down and without reading anything anyone else had written down. Even composers like Johann Sebastian Bach improvised on material they had written. Billie Holiday once said: 'everything that happened, happened by ear!' The Vikings weren't reading from charts when they blew their horns!
Charts do however give us a sense of the overall shape of piece of music or its ‘form’, such as ‘AABA’ where section A of the song will be labelled clearly, repeated before evolving into section B, then returning as A to close. Each section may be 8 bars and a whole song 32 bars. There are a small number of these patterns in jazz standards which will gradually become familiar as you listen to them. Try following them in ‘Fake Book’ or ‘Real Book’ collections. At this stage you probably know enough to follow the pattern of the melody. And as you play the song through a few times, listen carefully for bits that you’re not yet playing correctly against the recording and gradually iron out the inconsistencies. As we play we build an aural picture of how a song sounds, a finger/muscle picture of how it feels to play and a visual picture of the main dots on the chart, even if we don’t yet 'get' all of them. Eventually, when we’ve really learned a song, we’re playing from what neuroscientists call our ‘procedural memory’, buried deep in our brain’s ‘striatum’ and ‘cerebellum’ zones, or what guitarist Bill Frisell just calls our ‘bloodstream’. Once we’ve learned the tune, the score just becomes a set of cues to jog those memories.