Check this example which is already posted in the community shows a list of tasks for a user and also allows to complete the listed tasks.
http://community.jboss.org/people/bpmn2user/blog/2011/09/21/jbpm5-web-example
Check JbpmAPIUtil.java in the example
.The method List <TaskSummary> getAssignedTasks(String id) , shows how to get the details of task assigned to a user. Hope this helps