The SharePoint 2010 Software Development Kit (SDK) has been updated with new documentation, code samples, and IntelliSense XML files. You can get it here from the Microsoft Download Center. As always, the SDK is a free download.
The SDK now contains information for developing SharePoint Online solutions. For more information, check out the SharePoint Online Developer Center on MSDN. Recommended starting places are Developing SharePoint Online Solutions or SharePoint Online Development in 180 seconds (online video). You can also download the SharePoint Online for Office 365: Developer Guide.
The following topic describes how to download and install the SDK. You can also watch a video here. The current version of the SDK is 4763.1086. You’ll need to uninstall previous versions of the SDK before installing this new one.
You can set up the SDK on a machine that has SharePoint installed, or you can also set up the SDK on a remote development machine (e.g., Windows 7). Check out the article: Setting up the Development Environment on Windows Vista, Windows 7, and Windows Server 2008.