Vice-President Biden took the oath first, in the morning, at the Naval Observatory (which is also the official residence of the Vice President). He was sworn in by Sonya Sotomayor, Associate Justice of the United States Supreme Court:
At the Vice-President's request, there was a prayer before the swearing-in. This is not required by law, but is certainly a nice added touch. The Biden family was present.
President Obama was sworn in at the White House at 11:55 AM EDT. John Roberts, Chief Justice of the United States Supreme Court, administered the oath of office:
The Obama family was present. Chief Justice Roberts read the oath from a piece of paper and this time, no mistakes were made.
And with this simple act, the second term of the Obama/Biden administration has officially begun. For the first time in our Union's history, three consecutive two-term administrations with exactly the same ticket both times have been sworn-in: Clinton / Gore in 1993 and 1997, Bush / Cheney in 2001 and 2005 and now, Obama / Biden in 2009 and 2013!
The public inaugural ceremonies will take place tomorrow, January 21st, 2103 since today was a Sunday, and tomorrow both the President and the Vice-President will reaffirm their respective oaths of office - but make no mistake about it: Obama / Biden have already been sworn in and their second term has now begun.
My best wishes to the entire Obama administration for a sucessful second term in office.
This is also being covered in the press all over the place:
Talking Points Memo
ARD - Tagesschau (German)
ZDF Heute (German)
Die Welt (German)
Here screenshots of media coverage of the 2nd term oath (in random order):