Tecnicamente eso es todo del tutorial :c

resources/js/views/UserEdit.vue

@@ -0,0 +1,90 @@
+<template>
+    <div>
+        <div v-if="message" class="alert">{{ message }}</div>
+        <div v-if="!loaded">Loading...</div>
+        <form @submit.prevent="onSubmit($event)" v-else>
+            <div class="form-group">
+                <label for="username">Name</label>
+                <input id="username" v-model="user.name"/>
+            </div>
+            <div class="form-group">
+                <label for="email">Email</label>
+                <input id="email" type="email" v-model="user.email"/>
+            </div>
+            <div class="form-group">
+                <button type="submit" :disabled="saving">Update</button>
+                <button :disabled="saving" @click.prevent="onDelete($event)">Delete</button>
+            </div>
+        </form>
+    </div>
+</template>
+
+<style lang="scss" scoped>
+$red: lighten(red, 30%);
+$darkRed: darken($red, 50%);
+
+.form-group label {
+    display: block;
+}
+
+.alert {
+    background: $red;
+    color: $darkRed;
+    padding: 1rem;
+    margin-bottom: 1rem;
+    width: 50%;
+    border: 1px solid $darkRed;
+    border-radius: 5px;
+}
+</style>
+
+<script>
+import api from '../api/users';
+
+export default {
+    data() {
+        return {
+            message: null,
+            loaded: false,
+            saving: false,
+            user: {
+                id:    null,
+                name:  "",
+                email: "",
+            }
+        }
+    },
+    methods: {
+        onSubmit(event) {
+            this.saving = true;
+
+            api.edit(this.user.id, {
+                name: this.user.name,
+                email: this.user.email,
+            }).then((response) => {
+                this.message = 'User Updated';
+                setTimeout(() => this.message = null, 2000);
+                this.user = response.data.data;
+            }).catch((error) => {
+                console.log(error);
+            }).then(_ => this.saving = false);
+        },
+        onDelete(event) {
+            this.saving = true;
+            api.delete(this.user.id)
+            .then((response) => {
+                this.message = 'User Deleted';
+                setTimeout(() => this.$router.push({ name:'users.index' }), 2000);
+            });
+        }
+    },
+    created() {
+        api.find(this.$route.params.id).then((response) => {
+            this.loaded = true;
+            this.user = response.data.data;
+        }).catch((err) => {
+            this.$router.push({ name:'404' });
+        });
+    }
+};
+</script>