Someone has probably written a book on this. There were a lot of factors that lead to Google gaining dominance.
Some of the highlights:
1 - Microsoft let IE6 languish after capturing the market. This was strategic because they felt the Web threatened their dominance on the desktop.
2 - Mozilla attacked IE6 by promoting standards compliance and worked to clearly document web standards and compliance.
3 - Mozilla attacked IE6 by launching Firefox (formerly Phoenix) and focusing standards compliance.
4 - Apple introduced a platform (iPhone) that was rapidly adopted and incompatible with IE6, necessitating change
5 - Google saw Mozilla Firefox clawing back 25% market share from IE6
6 - Google leveraged the browser engine in Safari (the iPhone browser) to launch their own browser with a focus on performance.
7 - Google put ads for Chrome on Google Search which basically put them in Firefox and on all platforms.