Download tools. Downloading SQL Server Express is probably the quickest way to get a SQL database and development environment onto a Windows machine. For other platforms, try the MySQL package that includes developer tools. If you have MS Access on your machine, you can start learning SQL with that. Oracle also offers its Express version for free and provides SQL Developer in a separate download for accessing and managing it.
Visit a tutorial. Some great tutorials reside at W3Schools, SQL-Tutorial.net and firstSql.com. Take a little time to make sure the tutorial creator's style is one you can easily learn from. W3Schools tutorial includes a web form where you can submit SQL queries against a database and see the results online. If all you need is the basics of the language and you don't care about tools, using this will free you from having to carry out step one.
Do the exercises. Tutorials generally follow a regular pattern. They introduce a concept, provide some examples and then challenge the student with a few exercises. Even though the exercises take precious time, do as many as you can. You won't really know a computer language until you write some codes.
Read a book. Several books have been written for people in just your situation. Select books that cover just the basics, but which do so thoroughly. "SQL for Dummies" comes highly recommended as a quick introduction. According to reviews, "Sams Teach Yourself SQL in 24 Hours" by Ron Plew and Ryan Stephens delivers on its promise.