Create a document type in Umbraco called Download File and put this code into the template. When you want a user to download a file, direct them to example.com/downloadfile?id=####. The ID query string must be equal to a media items ID.

DownloadFile.cs

using Umbraco.Web;
using System.Web.Http;
using System.Web;
using System.IO;

namespace Examples.Service
{
    public class DownloadServiceController : Umbraco.Web.Mvc.SurfaceController
    {
        // Use this if you only want logged in users to access these methods.
        //[Umbraco.Web.WebApi.UmbracoAuthorize]
        //[HttpGet]

        /// /umbraco/surface/DownloadService/download?id=####&filename=document.doc
        /// <summary>
        /// Downloads an item from the Umbraco Media section to the users browser.
        /// </summary>
        /// <returns></returns>
        public void Download(int id, string fileName)
        {
            var media = Umbraco.TypedMedia(id);

            if (media != null)
            {
                // Get the physical path to the file.
                string filePath = HttpContext.Server.MapPath(media.Url);

                Download(filePath, fileName);
            }
        }

        /// /umbraco/surface/DownloadService/download?filepath=####&filename=document.doc
        /// <summary>
        /// Downsloads a file based on the files path to the users browser.
        /// </summary>
        /// <returns></returns>
        public void Download(string filePath, string fileName)
        {
            Response.ContentType = "application/force-download";
            Response.AppendHeader("content-disposition", "attachment; filename=" + fileName);

            // Write the file directly to the HTTP content output stream.
            Response.WriteFile(filePath);
            Response.End();
        }

        /// /umbraco/surface/DownloadService/download?buffer=####&filename=document.doc
        /// <summary>
        /// Turns a buffer into a downloadable file which is then sent to the users browser.
        /// </summary>
        /// <returns></returns>
        public void Download(byte[] buffer, string fileName)
        {
            Response.ContentType = "application/force-download";
            Response.AppendHeader("content-disposition", "attachment; filename=" + fileName);

            Response.BinaryWrite(buffer);
            Response.End();
        }

        /// /umbraco/surface/DownloadService/download?stream=####&filename=document.doc
        /// <summary>
        /// Turns a stream into a downloadable file which is then sent to the users browser.
        /// </summary>
        /// <returns></returns>
        public void Download(Stream stream, string fileName)
        {
            var memoryStream = new MemoryStream();
            stream.CopyTo(memoryStream);
            var buffer = memoryStream.ToArray();

            Download(buffer, fileName);
        }
    }
}