first shutdown jira:
go to your JIRA bin directory and:
./shutdown.sh

create a separate directory, outside your JIRA installation dir, to store the upgrade files:

mkdir upgradejira
cd upgradejira
wget http://www.atlassian.com/software/jira/downloads/binary/atlassian-jira-6.3.12-x64.bin
chmod a+x atlassian-jira-6.3.12-x64.bin
./atlassian-jira-6.3.12-x64.bin