Where do I start to understand the concepts students must internalize about fractions in the Common Core State Standards?

My suggestion is to go to the Illustrative Mathematics website and watch all 7 of the unit modules below. They are easy to understand, and really get you thinking about how you should present these concepts to your students.

Ask yourself:

What have I done in the past that will help students understand these ideas?

What manipulatives will help my students understand these ideas?. Or what representational drawings, area models, or number lines will help them make sense of these ideas?

What vocabulary words or "bridging lessons" should I present to help my struggling students or English Language Learners?

If our class created an ongoing bulletin board titled, "The Big Ideas About Fractions," what synthesized ideas MUST be on that bulletin board?

What evaluation tools will I use so I can see if each individual students understands these concepts?

http://www.illustrativemathematics.org/pages/fractions_progression