The easiest way to install a war file in Tomcat is to drop the war file in your TOMCAT_INSTALL/webapps directory. Tomcat will deploy it for you automatically.
If you want the contextPath to be 'wiki' then rename your war file to wiki.war before dropping it there.
Do you have your application in a WAR file (wiki.war)? If yes, then you simply need to copy wiki.war to the webapps directory of your Tomcat installation. After starting Tomcat, it will deploy your application automatically on http://<server>:<port>/wiki
To customize this, you need to edit the <Context> element of your webapp in server.xml. See the documentation for more info.