Install
Sextante is in the official plugin repository. Go to Plugins => Fetch Plugins, look for Sextante in the list, select it and click install.
In case it is not in the list, the main repository is probably missing. Go to the Repositories tab and add the following URL: http://plugins.qgis.org/plugins/plugins.xml
Enable
You also have to make sure it is enabled. Go to Plugins => Manage Plugins, and tick the Sextante entry in the list.
Newer version
The latest version for QGIS 1.8 is from January 2013. Since then, a lot of improvement has been made, but is only available with the current Nightly (aka master, 1.9, 2.0) and is there installed by default. Be aware that this is an unstable version of QGIS but may bring improvements.