Cross-component communication doesn't get much attention in the Vue.js docs, nor are there many tutorials that cover this subject. As components should be isolated, you should never access a component directly. This would tightly couple the components together, and thats exactly what you want to prevent doing.

Javascript has an excellent method for communication: events. Vue.js has a built-in event system, mainly used for parent-child communication. From the docs:

Although you can directly access a Vue instance’s children and parent, it is more convenient to use the built-in event system for cross-component communication. It also makes your code less coupled and easier to maintain. Once a parent-child relationship is established, you can dispatch and trigger events using each component’s event instance methods.

Their example code to illustrate the event system:

var parent = new Vue({

  template: '<div><child></child></div>',

  created: function () {

    this.$on('child-created', function (child) {

      console.log('new child created: ')

      console.log(child)

    })

  },

  components: {

    child: {

      created: function () {

        this.$dispatch('child-created', this)

      }

    }

  }

}).$mount()

Dan Holloran has recently written a piece on his struggle with cross-component messaging, in two pieces. This might be helpful to you if you need communication between components that have no parent-child relationship.

Another approach I have experience with (other than using events for communication), is using a central component registry that has a reference to the public API with an instance of a component bound to it. The registry handles requests for a component and returns its public API.

In the context of Vue.js, events would by my weapon of choice.