How to use Office 2010's co-authoring tools?

From Word 2010 Coauthoring Guide :

Step One – Install Word 2010
Co-authoring only works in Word 2010, so it will need to be installed on all computers you want to co-author with.

Step Two – Set up a Microsoft SkyDrive account
This comes for free with any Windows Live account. More info at: http://windowslive.com/online/skydrive.

Step Three – Create a folder on your Skydrive
Log in and create a new folder in your Skydrive to store speeches in. We use one account for the whole team, with a separate subfolder for each team. It is recommended you use a “protected” folder rather than a public folder – otherwise your evidence will be accessible by anyone.

Step Four – Find Your SkyDrive WebDAV Address
This is the unique WebDAV identifier for your SkyDrive. There are several ways to find this, including using the built-in “Save To Web” function in Word 2010. I think the easiest method is to log in to your Skydrive in your web browser, and then take note of the URL. It will look something like this:
http://cid-425e2847g321hh2e.skydrive.live.com/home.aspx
The WebDAV address is the alphanumeric code after “cid” – "425e2847g321hh2e".

Step Five – Setup SkyDrive as a network drive
There are several ways to map a network drive in Windows. For ease of use, it is recommended you set up a “batch” file in the following step. To do it manually, open Windows Explorer, right click on “Computer” and select “Map Network Drive.” Select a drive letter (we use Z), and in “Folder” put:
\\docs.live.net@SSL\425e2847g321hh2e\DebateFolder.
Make sure to replace the WebDAV address above with your own alphanumeric code, and the name of the folder you created instead of “DebateFolder”.
When it asks you for a username and password, use the information you selected when you signed up for Skydrive, and add “@hotmail.com” to the username:

Username: [email protected]
Password: yourpassword

That’s it! If you did everything correctly, you will now have access to your Skydrive account as a separate drive on your computer, accessible through Windows Explorer or Word. Now, to use co-authoring, just put a Word file on the server and open it simultaneously with 2 separate computers. Both users should then be able to make edits.

Step Six – Create a .bat file
Since reconnecting the Skydrive on each computer can be tedious, it’s easiest to write a batch file to automatically connect. To do this, create a new text file on your computer called, for example, “Skydrive.bat” Make sure that the file extension is .bat, not .txt. Insert the following lines of text:

net use z: \\docs.live.net@SSL\425e2847g321hh2e\DebateFolder * /user:[email protected] start z:

Make sure to replace the WebDAV address, folder name, drive letter, and email address with your own information. Save the file somewhere convenient. Now, when you double-click the .bat file, it should prompt you for your password, then automatically open the network drive in explorer.

Problems that can prevent co-authoring are listed in Why can’t I edit the server file?.
The following is a shortened extract of the article :

Another author is using a different version of Word

The new co-authoring functionality is available only in Word 2010 and Word for Mac 2011.

The file format is not compatible with the co-authoring functionality

The co-authoring functionality can be used with .docx files

Edit permissions have not been granted

Other features that can’t be used with the co-authoring functionality

The co-authoring functionality is not available if the document is marked as final or if it includes either of the following:

• Information Rights Management or Digital Rights Management
• Encryption
• ActiveX controls

The co-authoring functionality is not available if the document is a master document or a sub-document, or if the Store random numbers to improve Combine accuracy option is not selected.