UPDATE

The gwibber version with fixed Twitter OAuth is now in lucid-updates Running your update manager via either: System -> Administration -> Update Manager , (or sudo apt-get update && sudo apt-get upgrade) should trigger the update process.

The easiest way to grab the latest version of Gwibber is to add the ubuntu-desktop PPA (which includes the latest updates for desktop software, including Gwibber)

From command line:

sudo add-apt-repository ppa:ubuntu-desktop/ppa
sudo apt-get update
sudo apt-get upgrade

If you don't want the whole ubuntu-desktop ppa (which you may not - though it can be quite helpful to avoid issues of this nature in the future) you can simply add the Gwibber Daily PPA which will only provide the updates for Gwibber

sudo add-apt-repository ppa:gwibber-daily/ppa
sudo apt-get update
sudo apt-get upgrade

After the upgrade you will need to restart Gwibber:

gwibber-service restart

If that method does not work open the Gwibber interface then choose Gwibber->Quit and Launch it again either from the Message Indicator Applet or via Applications->Internet->Gwibber Social Client

Once Gwibber has restarted you will need to authenticate your Twitter account. Open the client and navigate to Edit->Accounts then click Authorize on your Twitter account in order to complete the process.

The Oauthcalypse caught me off guard too - even though I was watching the Countdown to OAuthcalypse I failed to relate that to Gwibber

Add the Ubuntu Desktop PPA

sudo add-apt-repository sudo add-apt-repository ppa:ubuntu-desktop/ppa

and update

sudo apt-get update && sudo apt-get upgrade\

then restart Gwibber

gwibber-service restart

[Source: WebUpd8]