Every supervisor should know to read and understand the general notes from the structural drawings, but there is more info than just that. Not enough of us field supervisors take the time to collect all of the project info. We to often rely on the superintendent to keep track of concrete submittals, additives, tolerances, and inspectors. You are the one in the trenches with the crew, not in the office. Shouldn't you be able to be the one that makes the decisions and answers the questions? You should empower yourself with knowledge.
• Plans - This is the obvious one, here you will find dimensions for layout, details to understand how it all ties together, and schedules to know sizes and reinforcing. Be sure your checking between all of the plans, Architectural's, Structural's, and M.E.P's.
• Submittals - These are the manufacturers information and sometimes installation instructions for all of the components and materials going into your project. Your concrete supplier will have turned in a Submittal of all the mix designs for approval by the Structural Engineer. This is information you need to know. It will tell you slump and air tolerances, unit weight, and all of the doses of the admixtures in that particular mix. This is critical information when dealing with inspectors and testers. Your knowledge of the concrete your pouring could be the difference between an NCR, rejected trucks or a smooth pour.
• Specifications - The Specs are the parameters of materials, building components, and their installation. The Architect and Engineers use these to define the outcome of the job. Before your concrete supplier turns in his submittal he reads the specs to know what his mix design needs to be. They are broken into numbered divisions per discipline. It might look at first glance like too much to take on, but just find your division (3 for concrete) and start reading. I always look for specifics like testing frequency, slump tolerances for different water reducers, approved curing procedures, and F number tolerances for slabs. The FF and FL tolerances are important to you so you can communicate them to the flatwork crew(assuming you're not the finisher supervisor).
Make sure up front, before a serious problem arises that you have done your due diligence in gathering all of the information related to your scope in the project. If you don't have immediate access to submittals and specs ask! I'm sure your Superintendent or Project Engineer will be both impressed and helpful getting you everything you need