How to read it
Every note the chart covers is on the staff, lowest to highest, with its fingering underneath. Filled keys are pressed; open ones stay up. Smaller diagrams beside a fingering are alternates. Notes are written the way they appear in your part, not at concert pitch.
Notes with two names
A♯ and B♭ are the same note, with the same fingering. The chart writes the flat on the staff and the sharp name under it, so you can find either one.
When to use an alternate
Alternates make some note changes smoother or fix a note that sits out of tune on your instrument. Learn the main fingering first, then ask your director which alternate fits the passage you are working on.