Preview:
Html:
Nota;para colocar el codigo Html solamente tipea !.

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <title>Document</title>
</head>
<body>
  <div id="app">
    {{mensaje}}
    <hr>
    <input type="button" @click="mostrar=!mostrar" value="Click">
    <input v-if="mostrar" v-model="mensaje2">
  </div>
<script src="https://cdnjs.cloudflare.com/ajax/libs/vue/2.0.3/vue.js"></script>
</body>
</html>

JavaScript:
const app = new Vue ({
el:"#app",
  data: {
    mensaje:"Aja",
    mensaje2:"Hola Bomboncito",
    mostrar:false
  }
})
Salida:
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