Updated October 22 2012: The final version of Office Web Apps has gone live.
In July 2012 Microsoft made Office 2013 Public Preview available for download. The accompanying Office Web Apps will also be updated with the final release early next year, but you can already access the preview if you know where to look.
Go to SkyDrive.com and log in with your Microsoft Account (formerly Microsoft Live ID).
Click the gear in the upper right corner and choose Options.
To the left you should find a setting for the preview version. Click it and enable it.
You can drag and drop to move files within SkyDrive, but you can also drag files from your computer into the browser window. The files will automatically upload. Right-clicking a folder or file will get you a menu from which you can delete and to other tasks.
To edit a document (Word, Excel, PowerPoint and OneNote is supported), just click it and it will open in the appropriate app. You can do simple editing online, for the full set of features you can easily open the document in the application on your computer.
To make a new document, simply choose the type from the Create menu in the upper left.
Tip: If you open an OneNote notebook in your local OneNote application, it will automatically sync between your devices and SkyDrive. Apps for iPhone, iPad and Android is available for free. OneNote is already built into Windows Phone. And there’s a special Metro version for Windows 8 in the new Windows Store. I have several notebooks on SkyDrive which I access online and through my iPad and Android phone.