disublayout.ascx

<%@ Control Language="C#" AutoEventWireup="true" CodeBehind="disublayout.ascx.cs" Inherits="Website.sublayouts.disublayout" %>
<%@ Register TagPrefix="sc" Namespace="Sitecore.Web.UI.WebControls" Assembly="Sitecore.Kernel" %>
<asp:Label runat="server" ID="demo" Text="initial text" />

disublayout.ascx.cs

using System;

using App.Abstract;

namespace Website.sublayouts
{
    public partial class disublayout : System.Web.UI.UserControl
    {
        public IFooService SomeDependency { get; set; }

        protected void Page_Load(object sender, EventArgs e)
        {
            demo.Text = SomeDependency.GetData();
        }
    }
}

namespace App.Abstract
{
    public interface IFooService
    {
        string GetData();
    }
}

namespace App.Concrete
{
    public class FooService : IFooService
    {
        public string GetData()
        {
            return "Modified at " + DateTime.Now.ToLongTimeString();
        }
    }
}

Global.asax

<%@Application Language='C#' Inherits="Website.Global" CodeBehind="Global.asax.cs" %>

Global.asax.cs

using Autofac.Integration.Web;
using Sitecore.Web;

namespace Website
{
    public class Global : Application, IContainerProviderAccessor
    {
        static IContainerProvider _containerProvider;

        public IContainerProvider ContainerProvider
        {
            get { return _containerProvider; }
        }
        
        public void Application_Start()
        {
            _containerProvider = new ContainerProvider(ObjectBuilder.Register());
        }
    }
}

ObjectBuilder.cs

using Autofac;

using App.Abstract;
using App.Concrete;

namespace Website
{
    public static class ObjectBuilder
    {
        public static IContainer Register()
        {
            var builder = new ContainerBuilder();

            builder.Register<IFooService>(c => new FooService());
            
            return builder.Build();
        }
    }
}