Absolute beginners start here at Learning Mandarin Chinese: A Step-By-Step Guide. By far the most succinct, basic, and comprehensive guide to introductory Mandarin.
You can take a free online class at Memrise.
The Chinese Outpost also has a free Intro to Mandarin class.
Kids Chinese Podcast A podcast-based Chinese course for children and adults
Many local community colleges and universities also offer introductory Chinese classes.