I just had to convert a big SQL Server DB 2005/2008 into a MySQL DB 5+, and decided to share my (successful) experience.
Ultimately you’ll want to use some tool to automate the process, specially because you don’t want to deal with data-type conversions (i.e. SQL Server’s varchar is not the same as MySQL varchar, etc), foreign key constraints, etc.. I used SQLyog, which is a great (Windows) application. The trial version allows for the import of two tables (schema and data) at a time. I had to create a File DSN (ODBC) to connect to my remote MS SQL Server.