Sauce Labs provides a platform that allows users to run tests created in Selenium IDE (in HTML format) with Selenium RC by utilizing its Sauce IDE tool. To use this platform, users must save the test case and test suite as HTML files, ensuring they have the correct file names and extensions. Once saved, Sauce RC can be instructed on where to find these files, including the path to the test suite and result directory, start URL, and browser selection. With this setup, users can run their tests against multiple browsers using Sauce RC, making it a convenient solution for cross-browser testing.