first you should check whether your tomcat is running or not. Go to your browser and type "http://localhost:8080/"
;. Instead of 8080 replace it with the port your tomcat is running on. If it shows a welcome screen tomcat is running.
Then scroll down the welcome page and deploy your war file by browsing it in the text field given at the page. Your project is deployed now. To check whether it is deployed go to "tomcat manager" link on the welcome page. It shows you what all projects are deployed.
if it is asking for a password add a user in tomcat_users.xml in conf folder in tomcat installation directory.
ADD these lines
<user username="tomcat" password="s3cret" roles="manager"/>
in between <tomcat-users> tag.
and login as user=tomcat password=s3cret