A musical analysis of a piece should provide insight into how a particular piece of music works. Gauldin talks about the interaction of Formal Design and Tonal Structure as being essential to analysis. Another way to understand analysis is to find interactions between between different musical and structural elements, the small-scale event and the large-scale architecture.
Start with what you know…
You already know how to identify keys, chords with Roman numerals and figured bass, cadences, harmonic and melodic sequences, common progressions, rhythmic devices, tonicizations, and modulations. In a way, it is like you’ve learned basic grammar and sentence structure. Now you want to start using that knowledge to understand music in a larger sense. How does a composer articulate departure and return? How do thematic elements relate to each other? How does progression relate to key area? Or motive to key area? (there are many more questions to ask…)
The Big Picture(tm)
As you start to identify the the building blocks that you know, you’ll find that the labeling of each individual harmony is less important that identifying the overall function of progressions, finding the essential voice leading, or making connections between progressions and key areas. Sometimes you’ll have to infer certain harmonies, based on their placement in the phrase, or their relationship to other elements of the work. Inferring isn’t making things up. It’s making an educated assumption based on what you know and what you can identify.
As academic as things seem at this point, it is important to keep in mind that we’re now moving into learning about how music really works, as a whole, based on real music. The more you can learn through analysis of music, the more you learn about music. The more you learn about music, the better performer|composer|educator|music technologist|scholar you will be.