The simplest comment implementation I could come up with using Episerver Social with the "Alloy" demo site

CommentForm.html

<form method="post" action="/social/comments/add" id="commentForm">
    <input type="hidden" name="pageId" value="@Model.CurrentPage.ContentGuid"/>
    <input type="text" name="author" placeholder="Your name..."/>
    <textarea name="body" id="commentBody" placeholder="Your comment..."></textarea>
    <br/>
    <input type="submit" id="commentSubmitButton" disabled="disabled" style="opacity: 0.5;"  value="Submit" />
</form>

<div id="commentList">
        Loading comments...
</div>

<script>
    $(function () {

        var commentForm = $('#commentForm');
        var commentBody = $('#commentBody');
        var commentSubmitButton = $('#commentSubmitButton');

        commentBody.keyup(function () {
            bodyEmpty = commentBody.val().length == 0;
            commentSubmitButton.attr('style', 'opacity: ' + (bodyEmpty ? '0.5' : '1.0'));
            commentSubmitButton.prop('disabled', bodyEmpty);
        });

        commentForm.submit(function (e) {
            e.preventDefault();
            $.ajax({
                type: commentForm.attr('method'),
                url: commentForm.attr('action'),
                data: commentForm.serialize(),
                success: function (html) {
                    refreshComments(html);
                    document.getElementById("commentForm").reset();
                }
            });
        });

        // This happens on page load...
        $.ajax({
            type: "POST",
            url: '/social/comments/get?id=@Model.CurrentPage.ContentGuid',
            success: function (html) {
                refreshComments(html);
            }
        });
    });

    function refreshComments(html) {
        $('#commentList').html(html);
    }
</script>

CommentList.cshtml

@using EPiServer.Social.Comments.Core
@using EPiServer.Social.Common
@model ResultPage<Comment>


@foreach (var comment in Model.Results)
{
    <div class="comment">
        <blockquote>@comment.Body</blockquote>
        <div class="commentMeta">
            by @comment.Author
            on @comment.Created.ToLocalTime().ToString("MMM dd, yyyy 'at' h:mm tt")
        </div>
    </div>
}

<style>
    .comment {
        margin-bottom: 2em;
    }
    .comment blockquote {
        background-color: rgb(250,250,250);
        padding: 1em;
        margin-bottom: 2px;
    }
    .comment .commentMeta { 
        font-style: italic;
    }
</style>

SocialController.cs

using EPiServer.ServiceLocation;
using EPiServer.Social.Comments.Core;
using EPiServer.Social.Common;
using System;
using System.Collections.Generic;
using System.ComponentModel.DataAnnotations;
using System.Linq;
using System.Web;
using System.Web.Mvc;

namespace Demo1.Controllers
{
    public class SocialController : Controller
    {
        private const string ANONYMOUS_AUTHOR_NAME = "Anonymous Coward";
        readonly ICommentService commentService;

        public SocialController(ICommentService commentService)
        {
            this.commentService = commentService;
        }

        [Route("social/comments/add")]
        [HttpPost]
        public ActionResult AddComments(CommentSubmission commentSubmission)
        {
            if(ModelState.IsValid)
            {
                var comment = new Comment(
                    parent: Reference.Create(GetContentReference(commentSubmission.PageId)),
                    author: Reference.Create(commentSubmission.Author ?? ANONYMOUS_AUTHOR_NAME), // This should technically be a reference to the author, but a simple string works too
                    body: commentSubmission.Body,
                    isVisible: true
                );
                commentService.Add(comment);
            }

            return GetComments(commentSubmission.PageId);
        }

        [Route("social/comments/get")]
        [HttpPost]
        public ActionResult GetComments(Guid id)
        {
            var criteria = new Criteria<CommentFilter>
            {
                Filter = new CommentFilter
                {
                    Parent = Reference.Create(GetContentReference(id))
                },
                OrderBy = new List<SortInfo>
                {
                    new SortInfo(CommentSortFields.Created, false)
                }
            };
            var comments = commentService.Get(criteria);
            return PartialView("/Views/Shared/PagePartials/CommentList.cshtml", comments);
        }

        private string GetContentReference(Guid id)
        {
            return string.Concat("content://", id.ToString());
        }
    }

    public class CommentSubmission
    {
        [Required]
        public string Body { get; set; }
        public Guid PageId { get; set; }
        public string Author { get; set; }
    }
}