See http://docs.spring.io/spring/docs/4.0.x/spring-framework-reference/htmlsingle/#context-create.
The principle is to declare a ServletContextListener in the standard webapp descriptor (web.xml). Such a listener is indeed instantiated by the container and is called when the application is initialized and when it's destroyed.
Spring provides such a ServletContextListener: ContextLoaderListener which, as its name indicates, loads a Spring context when the webapp is initialized.