Edit: Due to the fact that this article is old, the installation instructions may not work anymore. In order to successfully install the latest version of LibreOffice, please access the libreoffice tag and open the latest article (the one on top).

The latest installation instructions for LibreOffice
Hello Linux Geeksters. As you may know, LibreOffice 4.1 stable has been released a while ago, with some bugfixes brought to the previous release candidate versions. To get a list of the features and improvements, see the release notes.
In this article I will show you how to install LibreOffice 4.1.0 on Ubuntu 13.10 Saucy Salamander, Ubuntu 13.04 Raring Ringtail, Ubuntu 12.04 Precise Pangolin, Linux Mint 16 Petra, Linux Mint 15 Olivia and Linux Mint 13 Maya, via PPA.
Because LibreOffice 4.1.0 is available via the official PPA (so you don’t have to download the packages and install them by hand anymore), installing it on Ubuntu and Linux Mint is easy. All you have to do is:
$ sudo add-apt-repository ppa:libreoffice/libreoffice-4-1
$ sudo apt-get update
$ sudo apt-get install libreoffice