Here are some useful resources for learning and using git and GitHub.

Books

• Pro Git – excellent book on git; well illustrated with how the graph of commits changes with common operations; free PDF
• The Git Community Book – another very good book; this one is somewhat friendlier and more conversational than Pro Git ; free PDF *Note: on my most recent visit, the online version was in French; the PDF was in English, though

Online resources

• git's site
• Atlassian's git tutorials -- great tutorials presented by the people behind BitBucket (a GitHub competitor), JIRA (issue tracking), and Confluence (wiki)
• another one that is more game-like, with a couple dozen exercises
• Think Like a Git - "My goal with this site is to help you, Dear Reader, understand what those smug bastards are talking about."
• Git from the Bottom Up - all the gory details on git internals

GUI clients

• SourceTree – Atlassian's free GUI client for Mac and Windows; however, recent versions require an Atlassian login to use
• GitHub has clients for Mac and Windows that closely integrate with the GitHub site
• most IDEs and many programmer's editors include git integration or git plugins of varying quality and feature set (eg, IntelliJ, Netbeans, Sublime Text, others)