Databricks users can export dataframes to CSV files using four different methods, each with its own advantages and requirements. The first method involves using Databricks Notebook to download or export data from DBFS, while the second method uses the command-line interface (CLI) to transfer existing CSV files between DBFS locations. The third method employs JSpark through the command line to export results to a local machine, and the fourth method utilizes external client tools like Visual Studio Code's Databricks extension for easy file browsing. While each method has its own trade-offs, Census is suggested as an alternative that simplifies data export without requiring API interaction or extensive setup.