The Book Industry Study Group (BISG) has led the industry approach to expanding ISBNs from 10 to 13 digits. The BISG has made available a special site (Are You Ready for ISBN-13?) which provides a comprehensive overview of the new 13-digit ISBN - why it is necessary, how and when to get ready, etc. The introduction provided by this website follows:
The ISBN provides a standard way to identify books in global trade. In 2007, the publishing industry began using 13-digit ISBNs, phasing out the use of 10-digit ISBNs.
This change affected everyone who uses ISBNs throughout the world.
The questions and answers included on this page relate to how Lightning Source has implemented support for the 13-digit ISBN and how you can take advantage of these changes.

No. LSI plans to support both 10 and 13-digit identifiers indefinitely. Consequently, it will never be necessary for you to explicitly change any 10-digit ISBNs to 13-digit ISBNs.
Since LSI catalogs will be published with BOTH 10-digit and 13-digit ISBNs (for titles published initially with a 10-digit ISBN or published initially with a 13-digit ISBN which begins with 978), it is not necessary for you to explicitly change any of your ISBNs in order to support orders for your titles. In effect, LSI is automatically doing this for you while simultaneously preserving the ability of any retailer to access your books via 10 or 13-digit ISBNs.
All publisher compensation and invoice reporting has been delivered with both 10 and 13-digit identifiers since 1/1/2006.
If you do decide to change your title's official ISBN from 10-digits to its 13-digit equivalent, LSI will continue to provide both 10 and 13-digit support for ordering, invoicing, etc. In fact, any ISBN change you make will be transparent to both LSI and ordering customers since LSI provides both 10 and 13-digit identifiers for all appropriate titles.

The only difference between a 979 and a 978 ISBN is that a 979 title does not have a 10-digit equivalent (i.e. you cannot convert a 13-digit 979 ISBN to a 10-digit ISBN as you can with a 13-digit 978 ISBN). As 13-digit 979 ISBNs are introduced, your catalog will have a mixture of 978 and 979 ISBNs in the 13-digit ISBN location; 979 ISBNs will have spaces (blanks) in the 10-digit ISBN location of their catalog record.

LSI does not determine or participate in any ISBN prefix assignment. Since there is no fixed relationship between 978 and 979 prefixed ISBNs, it is highly unlikely that existing ISBN prefixes will be retained. However, please consult your issuing ISBN provider or BISG for specifics regarding your situation.

LSI already prints 13-digit ISBN barcodes on the back cover of all books (it is also called the EAN). However, the human-readable number just above the ISBN will remain the same as originally provided to LSI. While the BISG recommends that new printings of 10-digit books be altered to print both 10 and 13-digit ISBNs in human readable form on the back cover and on the copyright page, LSI does not recommend this change for POD titles, since the barcode already complies with 13-digit standards. If you elect to have the human readable portion changed on the back cover and/or copyright page you may resubmit your changed content as a revision to LSI or request that LSI perform the revision directly on your behalf. Standard revision fees will apply for each title changed.

LSI already prints 13-digit ISBN barcodes on the back cover of all books (it is also called the EAN). However, the human-readable number just above the ISBN will remain the same as originally provided to LSI. While the BISG recommends that new printings of 10-digit books be altered to print both 10 and 13-digit ISBNs in human readable form on the back cover and on the copyright page, LSI does not recommend this change for POD titles, since the barcode already complies with 13-digit standards. If you elect to have the human readable portion changed on the back cover and/or copyright page you may resubmit your changed content as a revision to LSI or request that LSI perform the revision directly on your behalf. Standard revision fees will apply for each title changed.

ISBN.org provides an ISBN-13 Online Converter. In addition to converting ISBNs one at a time, this site also provides information on converting batches of ISBNs.

LSI plans to support both 10 and 13-digit identifiers indefinitely.
Books initially published with a 10-digit ISBN will always be available for order via both 10 and 13-digit ISBN, since their 10 and 13-digit ISBN identifiers are algorithmically interchangeable. Books published with a 13-digit ISBN starting with 978 will also be orderable via both 10 and 13-digit ISBN, since the 10-digit ISBN is interchangeable with a 13-digit ISBN beginning with 978. Books published with a 13-digit ISBN starting with anything other than 978 (e.g. 979) will not be orderable via a 10-digit equivalent ISBN. 979 ISBNs will begin being issued after 2007, according to the BISG standards committee.

Historically, the assignment of an ISBN to each eBook format has been handled differently by the publishing community. Some publishers assign an ISBN to each eBook format; other publishers assign a single ISBN at the eBook level (a single ISBN for all formats); and still other publishers do not assign a separate ISBN at all for an eBook, preferring instead to reference the eBook by its print ISBN counterpart. Because of this diversity in ISBN assignment, LSI has always assigned its own distinct identifier known as a SKU. This is a 10-digit identifier with a check-digit structure mimicking an ISBN, but which is not a registered ISBN. Every distinct format of every eBook is assigned a distinct SKU.

LSI will continue to assign these 10-digit SKUs to all eBook formats and provide these ordering SKU identifiers in all eBook catalogs. LSI will also provide the publisher assigned ISBN (10 or 13-digit) and parent ISBN. This will mean that the 940FIXED format is altered slightly to include space for the 13-digit identifiers. The altered catalog format will be referred to as the 940FIXED13 format.
What documentation will be available to help me understand what needs to be changed?
LSI's eBusiness with Lightning Source suite of documentation has been updated to describe the changes being made to support 13-digit ISBNs. Specifically, the eBook Integration Guide (eBusiness with Lightning Source: Part 5 - Guide 2) has been updated to describe the catalog changes necessary to communicate SKU and 13-digit ISBN information.