Create a new httpHandler inside your ASP.NET project. Apply the following code (VB) to the handler file:

Public Class AttachmentDownload
    Implements System.Web.IHttpHandler

    Sub ProcessRequest(ByVal context As HttpContext) Implements IHttpHandler.ProcessRequest

        ' pass an ID through the query string to append a unique identifer to your downloadable fileName

        Dim fileUniqueId As Integer = CInt(context.Request.QueryString("id"))

        ' file path could also be something like "C:\FolderName\FilesForUserToDownload

        Dim filePath As String = "\\ServerName\FolderName\FilesForUserToDownload"
        Dim fileName As String = "UserWillDownloadThisFile_" & fileUniqueId
        Dim fullFilePath = filePath & "\" & fileName
        Dim byteArray() As Byte = File.ReadAllBytes(fullFilePath)

        ' promt the user to download the file

        context.Response.Clear()
        context.Response.ContentType = "application/x-please-download-me" ' "application/x-unknown"
        context.Response.AppendHeader("Content-Disposition", "attachment; filename=" & fileName)
        context.Response.BinaryWrite(byteArray)
        context.Response.Flush()
        context.Response.Close()
        byteArray = Nothing

    End Sub

    ReadOnly Property IsReusable() As Boolean Implements IHttpHandler.IsReusable
        Get
            Return False
        End Get
    End Property

End Class

You can call the handler from code behind, or from a client side language. In this example I am using a javascript which will call the handler.

function openAttachmentDownloadHandler(fileId) {

    // the location of your handler, and query strings to be passed to it

    var url = "..\\_Handlers\\AttachmentDownload.ashx?";
    url = url + "id=" + fileId;

    // opening the handler will run its code, and it will close automatically
    // when it is finished. 

    window.open(url);

} 

Now attach that assign the javascript function to a button click event on a clickable element in your web form. For example:

<asp:LinkButton ID="lbtnDownloadFile" runat="server" OnClientClick="openAttachmentDownloadHandler(20);">Download A File</asp:LinkButton>

Or you can call the javascript function from the code behind as well:

ScriptManager.RegisterStartupScript(Page,
                Page.GetType(),
                "openAttachmentDownloadHandler",
                "openAttachmentDownloadHandler(" & fileId & ");",
                True)

Now when you click your button the httpHandler will get your file to the browser and ask the user if they would like to download it.