First create a Ubuntu Virtual Machine on Windows Azure and be sure it is running. Be sure to have SSH connection enabled working with your VM.

Once you can remote into your Ubuntu Linux VM over SSH try the following steps:

1. Installing Oracle Java SDK 

# sudo apt-get install openjdk-7-jre

2. Installing Tomcat 7:

#sudo apt-get install tomcat7

Creating config file /etc/default/tomcat7 with new version
Adding system user `tomcat7' (UID 106) ...
Adding new user `tomcat7' (UID 106) with group `tomcat7' ...
Not creating home directory `/usr/share/tomcat7'.
 * Starting Tomcat servlet engine tomcat7 [ OK ]
Setting up authbind (1.2.0build3) ...

3. Adding new Endpoint to your VM for Tomcat:

After that you can add a new Endpoint at port 8080 in your Ubuntu VM 

4. Test Tomcat:

Once endpoint is configured you can test your Tomcat installation as just by opening the VM URL at port 8080 as below:

5. Install other Tomcat components:

# sudo apt-get install tomcat7-admin

# sudo apt-get install tomcat7-docs

# sudo apt-get install tomcat-examples

# sudo apt-get install tomcat-user

6. Setting Tomcat specific environment variables into setenv.sh @ /usr/share/tomcat7/bin/setenv.sh

root@ubuntu12test:~# vi /usr/share/tomcat7/bin/setenv.sh
export CATALINA_BASE=/var/lib/tomcat7
export CATALINA_HOME=/usr/share/tomcat7

Verifying setenv.sh

root@ubuntu12test:~# cat /usr/share/tomcat7/bin/setenv.sh
export CATALINA_BASE=/var/lib/tomcat7
export CATALINA_HOME=/usr/share/tomcat7

7. Shutdown Tomcat:

 root@ubuntu12test:~# /usr/share/tomcat7/bin/shutdown.sh
 Using CATALINA_BASE: /var/lib/tomcat7
 Using CATALINA_HOME: /usr/share/tomcat7
 Using CATALINA_TMPDIR: /var/lib/tomcat7/temp
 Using JRE_HOME: /usr
 Using CLASSPATH: /usr/share/tomcat7/bin/bootstrap.jar:/usr/share/tomcat7/bin/tomcat-juli.jar
 
8. Start Tomcat:

 root@ubuntu12test:~# /usr/share/tomcat7/bin/startup.sh
 Using CATALINA_BASE: /var/lib/tomcat7
 Using CATALINA_HOME: /usr/share/tomcat7
 Using CATALINA_TMPDIR: /var/lib/tomcat7/temp
 Using JRE_HOME: /usr
 Using CLASSPATH: /usr/share/tomcat7/bin/bootstrap.jar:/usr/share/tomcat7/bin/tomcat-juli.jar


9. Tomcat Administration:

 Edit /etc/tomcat7/tomcat-users.xml to setup your admin credentials
   root@ubuntu12test:~# vi /etc/tomcat7/tomcat-users.xml

10. My Tomcat configuration looks likes as below:

root@ubuntu12test:~# cat /etc/tomcat7/tomcat-users.xml
<tomcat-users>
 <role rolename="manager"/>
 <role rolename="admin"/>
 <role rolename="manager-gui"/>
 <role rolename="manager-status"/>
 <user username="tomcat_user" password="tomcat_password" roles="manager,admin,manager-gui,manager-status"/>
</tomcat-users>

Verifying Tomcat Administration: