Download the xpi file from one of the links below by just clicking on the link and then saving the file.

For Thunderbird versions before b4pre of 2009/09/10, e.g. Thunderbird 3.0 beta 3, use version 0.6.2:
Version 0.6.2 of CompactHeader

For Thunderbird versions starting with b4pre of 2009/09/10, e.g. Thunderbird 3.0 beta 4, use version 0.7.0 or newer:
Version 0.8.3 of CompactHeader

For Thunderbird versions starting with 3.0pre of about 2009/10/20, use version 0.9.0 or newer:
Version 1.2.4 of CompactHeader

For Thunderbird versions starting with 5.0beta1, use version 1.2.5beta1 or newer:
Version 1.2.5beta1 of CompactHeader

There is also an experimental version with sidebar support:
Version 1.3.0beta6 of CompactHeader