How do I make a striped v-data-table in Vuetify?

Expanding Boussadjra Brahim's answer. Here is some css for styling the header and footer globally

<style>
  tbody tr:nth-of-type(even) {
    background-color: rgba(236, 237, 237);
  }

  tbody tr:nth-of-type(odd) {
    background-color: rgb(250 ,250, 250);
  }

  .v-data-table-header {
    background-color: rgba(182, 183, 187);
    color: white;
  }

  .v-data-footer {
    background-color: rgb(250 ,250, 250);
  }

  .theme--light.v-data-table thead tr th {
    color: white;
  }
</style>

You could achieve that by using the following CSS rule :

tbody tr:nth-of-type(odd) {
   background-color: rgba(0, 0, 0, .05);
 }

new Vue({
  el: '#app',
  data() {
    return {
      headers: [{
          text: 'Dessert (100g serving)',
          align: 'left',
          sortable: false,
          value: 'name'
        },
        {
          text: 'Calories',
          value: 'calories'
        },
        {
          text: 'Fat (g)',
          value: 'fat'
        },
        {
          text: 'Carbs (g)',
          value: 'carbs'
        },
        {
          text: 'Protein (g)',
          value: 'protein'
        },
        {
          text: 'Iron (%)',
          value: 'iron'
        }
      ],
      desserts: [{
          name: 'Frozen Yogurt',
          calories: 159,
          fat: 6.0,
          carbs: 24,
          protein: 4.0,
          iron: '1%'
        },
        {
          name: 'Ice cream sandwich',
          calories: 237,
          fat: 9.0,
          carbs: 37,
          protein: 4.3,
          iron: '1%'
        },
        {
          name: 'Eclair',
          calories: 262,
          fat: 16.0,
          carbs: 23,
          protein: 6.0,
          iron: '7%'
        },
        {
          name: 'Cupcake',
          calories: 305,
          fat: 3.7,
          carbs: 67,
          protein: 4.3,
          iron: '8%'
        },
        {
          name: 'Gingerbread',
          calories: 356,
          fat: 16.0,
          carbs: 49,
          protein: 3.9,
          iron: '16%'
        },
        {
          name: 'Jelly bean',
          calories: 375,
          fat: 0.0,
          carbs: 94,
          protein: 0.0,
          iron: '0%'
        },
        {
          name: 'Lollipop',
          calories: 392,
          fat: 0.2,
          carbs: 98,
          protein: 0,
          iron: '2%'
        },
        {
          name: 'Honeycomb',
          calories: 408,
          fat: 3.2,
          carbs: 87,
          protein: 6.5,
          iron: '45%'
        },
        {
          name: 'Donut',
          calories: 452,
          fat: 25.0,
          carbs: 51,
          protein: 4.9,
          iron: '22%'
        },
        {
          name: 'KitKat',
          calories: 518,
          fat: 26.0,
          carbs: 65,
          protein: 7,
          iron: '6%'
        }
      ]
    }
  }
})
tbody tr:nth-of-type(odd) {
  background-color: rgba(0, 0, 0, .05);
}
<script src="https://cdn.jsdelivr.net/npm/babel-polyfill/dist/polyfill.min.js"></script>
<script src="https://cdn.jsdelivr.net/npm/vue/dist/vue.js"></script>
<script src="https://cdn.jsdelivr.net/npm/[email protected]/dist/vuetify.min.js"></script>
<link rel="stylesheet" type="text/css" href="https://fonts.googleapis.com/css?family=Roboto:100,300,400,500,700,900|Material+Icons">
<link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/vuetify.min.css">
<div id="app">
  <v-app id="inspire">
    <v-data-table :headers="headers" :items="desserts" class="elevation-1">
      <template slot="items" slot-scope="props">
        <td>{{ props.item.name }}</td>
        <td class="text-xs-right">{{ props.item.calories }}</td>
        <td class="text-xs-right">{{ props.item.fat }}</td>
        <td class="text-xs-right">{{ props.item.carbs }}</td>
        <td class="text-xs-right">{{ props.item.protein }}</td>
        <td class="text-xs-right">{{ props.item.iron }}</td>
      </template>
    </v-data-table>
  </v-app>
</div>