First, you need to choose the icon theme that you want to use. All of the available themes can be previewed at http://www.insanejournal.com/moodlist.bml . (Note: InsaneJournal does plan to include more mood icon themes in the near future) .
Many clients available for download include the ability to add a mood icon to your journal entries. For more information about your preferred client, consult its documentation or its menu options. See http://www.insanejournal.com/support/faqbrowse.bml?faqid=129 for information on downloading a client. (Note: Not all LiveJournal clients are supported by InsaneJournal)