Developers heavily rely on Application Programming Interfaces (APIs) from libraries to build their software. As software evolves, developers may need to replace the used libraries with alternate libraries, a process known as library migration. Doing this manually can be tedious, time-consuming, and prone to errors. Automated migration techniques can help alleviate some of this burden. However, designing effective automated migration techniques requires understanding the types of code changes required to transform client code that used the old library to the new library. This paper contributes an empirical study that provides a holistic view of Python library migrations, both in terms of the code changes required in a migration and the typical development effort involved. We manually label 1,902 migration-related code changes in 335 Python library migrations from 311 client repositories spanning 141 library pairs from 35 domains. Based on our labeled data, we derive a taxonomy for describing migration-related code changes, PyMigTax. Leveraging PyMigTax and our labeled data, we investigate various characteristics of Python library migrations, such as the types of program elements and properties of API mappings, the combinations of types of migration-related code changes in a migration, and the typical development effort required for a migration. Our findings highlight various potential shortcomings of current library migration tools. For example, we find that 40% of library pairs have API mappings that involve non-function program elements, while most library migration techniques typically assume that function calls from the source library will map into (one or more) function calls from the target library. As an approximation for the development effort involved, we find that, on average, a developer needs to learn about 4 APIs and 2 API mappings to perform a migration, and change 8 lines of code. However, we also found cases of migrations that involve up to 43 unique APIs, 22 API mappings, and 758 lines of code, making them harder to manually implement. Overall, our contributions provide the necessary knowledge and foundations for developing automated Python library migration techniques.