Accessing and querying REST APIs with the Sqlyze plugin in Grafana involves using SQL to treat APIs as database tables, allowing for integration with various data sources, including NoSQL and document databases. The process requires installing an ODBC driver, such as the CData API driver, and setting up a data source in Grafana with necessary paths and API keys. The example provided uses ClickUp, a productivity tool, to demonstrate querying hierarchical data structures by creating template variables for different levels like Team, Space, and List, which are then used to filter and display tasks in Grafana dashboards. This method allows for creating interactive dashboards that integrate API data seamlessly, with potential applications beyond ClickUp, including tools like Jira, available for Grafana Cloud or Enterprise license users. The Sqlyze Enterprise plugin thus facilitates versatile data querying capabilities in Grafana, supporting SQL, NoSQL, document databases, and REST APIs.