Here’s an answer for the current libertine
version of 2014/11/25, since lockstep’s answer doesn’t work anymore with this current version (probably due to the changes in maintainer and conception since 2011).
Generally, Linux Libertine’s digits are either proportional (different widths) or tabular (same widths), and either oldstyle (different heights) or lining (same heights):

By default, i.e. if you don’t change anything, libertine
uses tabular lining figures.
You can specify the style of numbers in three different ways, which have different ranges.
Package options – global effect
oldstyle
(or osf
) for old-style figures
lining
(or nf
or lf
) for lining figures
proportional
(or p
) for varying-width figures
tabular
(or t
) for fixed-width figures
These apply to the entire document. Of course, it only makes sense to specify either oldstyle
or lining
, and either proportional
or tabular
. Example:
\usepackage[oldstyle, proportional]{libertine}
\fontfamily{…}
– local effect
This way is not described in the libertine
documentation.
- proportional oldstyle figures:
\fontfamily{LinuxLibertineT-OsF}\selectfont 123
- proportional lining figures:
\fontfamily{LinuxLibertineT-LF}\selectfont 123
- tabular oldstyle figures:
\fontfamily{LinuxLibertineT-TOsF}\selectfont 123
- tabular lining figures:
\fontfamily{LinuxLibertineT-TLF}\selectfont 123
These commands are placed in the document body, not in the preamble, and they change the font starting at the point where they’re placed. For more details on how to use these commands, have a look at the LaTeX answer to How do I use a particular font for a small section of text in my document?. Example:
123 tabular lining figures (default) up to here
\fontfamily{LinuxLibertineT-LF}\selectfont
123 proportional lining figures from now on
Macro – small, selective effect
\oldstylenums{123}
\liningnums{123}
\proportionalnums{123}
\tabularnums{123}
These macros only change the style of the numbers in the argument. Example:
123 tabular lining figures (default), but then \oldstylenums{123
(still tabular) oldstyle figures} and back to 123 tabular lining
figures