Installation has been designed to be as pain free as possible. However there are some additional checks you can do before installation to ensure that everything runs as smoothly as possible.

The first tip for installation is to check permissions. If you've already installed extensions on your Joomla! site then chances are your permissions are mostly correctly. JLibMan is a bit different to other extensions in that it provides an "installer adapter" for Joomla! 1.5 which means that it needs write access to a specific place.  

Please ensure that the folder: /libraries/joomla/installer/adapters is writeable by your Joomla! install.

Alternatively, you can copy the file from /administrator/components/com_jlibman/include/library.php to /libraries/joomla/installer/adapters to complete installation manually.