This is the solution for Tomcat 7.0
Step 1:
  Create war file  for your webapp/servlets.
  If you are using Eclipse, File->Export->Web->WAR file, and save it to a known location.
Step 2:
  Find out the home folder for your tomcat.
  For that, go to tomcat/apache-tomcat-7.0.41/bin and execute ./startup.sh
  This will print out couple of global variable names.
  Note down the one for CATALINA_HOME.
Step 3:
  Copy the war file from Step 1 in CATALINA_HOME/webapps
Step 4:
  Next, Create an xml file in CATALINA_HOME/conf/{Engine}/localhost/MyServlets.xml : 
<?xml version="1.0" encoding="ISO-8859-1" standalone="no"?>
<Context deployOnStartup="true" docBase="/home/ubuntu/Downloads/apache-tomcat-7.0.42/webapps/" reloadable="true">
<Manager pathname=""/>
</Context>
Change docBase to point to location where you copied the war file in Step 3.
Now, you can go go to tomcat/apache-tomcat-7.0.41/bin and execute ./startup.sh.
Your servlets will be automatically started.
Hope this helps.