1.Backup all your data before you start:
tar zcvf jforum.tar.gz /path/to/old/jforum
pg_dump jforum > /tmp/jforum.bak

2.Unpack jforum-2.3.2.war

3.Stop JForum.

4.Copy or upload only these new jar files into jforum's WEB-INF/lib:

commons-io-2.1.jar

commons-lang3-3.0.1.jar

ehcache-core-2.4.6.jar 

jdom-1.1.1.jar         

jforum-2.3.2.jar

lucene-analyzers-3.4.0.jar

lucene-core-3.4.0.jar

lucene-highlighter-3.4.0.jar

lucene-memory-3.4.0.jar

lucene-queries-3.4.0.jar

mysql-connector-java-5.1.18.jar

quartz-2.1.0.jar

slf4j-api-1.6.2.jar

slf4j-log4j12-1.6.2.jar

5.Remove the old version of the above jar files

commons-io-2.0.1.jar

commons-lang-2.6.jar

ehcache-core-2.4.2.jar        

jforum-2.3.1.jar

lucene-analyzers-3.3.0.jar

lucene-core-3.3.0.jar

lucene-highlighter-3.3.0.jar

lucene-memory-3.3.0.jar

lucene-queries-3.3.0.jar

mysql-connector-java-5.1.17.jar

quartz-2.0.2.jar

slf4j-api-1.6.1.jar

slf4j-log4j12-1.6.1.jar

6.Replace the following files with the one from new version:
WEB-INF/config/database/generic/generic_queries.sql
WEB-INF/config/database/*/*_db_struct.sql
WEB-INF/config/SystemGlobals.properties
WEB-INF/config/modulesMapping.properties
WEB-INF/config/urlPattern.properties

7.Run database upgrade script located under jforum-2.3.2/upgrade/2.3.2

8.Replace template files for jQuery 1.6.4:

/templates/default/forum_list.htm

/templates/default/post_form.htm

/templates/default/post_show.htm

/templates/default/topic_review.htm

/templates/default/admin/config_list.htm

/templates/default/admin/search_stats_list.htm

As follows:

<script type="text/javascript" src="http://code.jquery.com/jquery-1.6.4.min.js"></scrip>

9.Copy admin template update:

/templates/default/admin/admin_welcome.htm

/templates/default/admin/bottom.htm

Or add it yourself:

<iframe src="${contextPath}/ping_session.jsp" height="0" width="0" frameborder="0" scrolling="no" title="session keeper"></iframe>

10.Delete old version Lucene's index files under WEB-INF/jforumLuceneIndex

11.Start JForum.

12.Login as Admin user and rebuild the Lucene index from Admin Control Panel.

13.Check if JForum is working smoothly

14.Done.