addBayOrder(){

      this.num += 1; 

      this.orders.push({

        price: this.price,
        count: this.count,
        id: this.num 
        
      });
}

<button class="order-form__btn order-form__btn-bay" 
            v-on:click="addBayOrder">Купить
</button>

export default {
  name: 'app',
  data () {
    return {
      
      price: 0,
      count: 0,
      num: 0,
      orders: [],
     
    }
  },

  methods:{

    addBayOrder(){
      this.num += 1; 
      this.orders.push({
        price: this.price,
        count: this.count,
        id: this.num 
      });
    },

  computed:{
    summary(){
      return this.price*this.count;
    } 
  }

event.preventDefault();