To pull the Organic Traffic, you can look for the "Traffic Sources -> Search Engines - Natural" report. To check for keywords seached, you can also check the "Traffic Sources -> Search Keywords - Natural".
The "Site Metrics -> Key Metrics" is a good report to start to look for general traffic trend on your website. Further you can modify for metrics to be evaluated.
To analyze a drop, there are 2 ways to go about:
- Anomaly Detection and Contribution Analysis. Articles with details mentioned at bottom
- Raw data analysis (Data Feeds). Documentation page mentioned below