Edit in JSFiddle

<div id="app">
  <ul>
    <li class="user" v-repeat="users" v-transition>
      <span>{{name}} - {{email}}</span>
      <button v-on="click:removeUser(this)">X</button>
    </li>
  </ul>
  <form id="form" v-on="submit:addUser">
    <input v-model="newUser.name">
    <input v-model="newUser.email">
    <input type="submit" value="Add User">
  </form>
  <ul class="errors">
    <li v-show="!validation.name">Name cannot be empty.</li>
    <li v-show="!validation.email">Please provide a valid email address.</li>
  </ul>
</div>

var baseURL = 'https://vue-demo.firebaseIO.com/'
var emailRE = /^(([^<>()[\]\\.,;:\s@\"]+(\.[^<>()[\]\\.,;:\s@\"]+)*)|(\".+\"))@((\[[0-9]{1,3}\.[0-9]{1,3}\.[0-9]{1,3}\.[0-9]{1,3}\])|(([a-zA-Z\-0-9]+\.)+[a-zA-Z]{2,}))$/

/**
 * Setup firebase sync
 */

var Users = new Firebase(baseURL + 'users')

Users.on('child_added', function (snapshot) {
  var item = snapshot.val()
  item.id = snapshot.key()
  app.users.push(item)
})

Users.on('child_removed', function (snapshot) {
  var id = snapshot.key()
  app.users.some(function (user) {
    if (user.id === id) {
      app.users.$remove(user)
      return true
    }
  })
})

/**
 * Create Vue app
 */

var app = new Vue({

  // element to mount to
  el: '#app',

  // initial data
  data: {
    users: [],
    newUser: {
      name: '',
      email: ''
    }
  },

  // computed property for form validation state
  computed: {
    validation: function () {
      return {
        name: !!this.newUser.name.trim(),
        email: emailRE.test(this.newUser.email)
      }
    },
    isValid: function () {
      var validation = this.validation
      return Object.keys(validation).every(function (key) {
        return validation[key]
      })
    }
  },

  // methods
  methods: {
    addUser: function (e) {
      e.preventDefault()
      if (this.isValid) {
        Users.push(this.newUser)
        this.newUser.name = ''
        this.newUser.email = ''
      }
    },
    removeUser: function (user) {
      new Firebase(baseURL + 'users/' + user.id).remove()
    }
  }
})

body {
  font-family: Helvetica, Arial, sans-serif;
}

ul {
  padding: 0;
}

.user {
  height: 30px;
  line-height: 30px;
  padding: 10px;
  border-top: 1px solid #eee;
  overflow: hidden;
  transition: all .25s ease;
}

.user:last-child {
  border-bottom: 1px solid #eee;
}

.v-enter, .v-leave {
  height: 0;
  padding-top: 0;
  padding-bottom: 0;
  border-top-width: 0;
  border-bottom-width: 0;
}

.errors {
  color: #f00;
}