Code:

function DownloadFile(const Url: string; destFName: string): string;
var
  NetHandle: HINTERNET;
  UrlHandle: HINTERNET;
  Buffer: array[0..1024] of Char;
  BytesRead: dWord;
  f: File;
  i: longint;
begin
  Result := '';
  NetHandle := InternetOpen('Delphi ', INTERNET_OPEN_TYPE_PRECONFIG, nil, nil, 0);
  if Assigned(NetHandle) then  begin
    UrlHandle := InternetOpenUrl(NetHandle, PChar(Url), nil, 0, INTERNET_FLAG_RELOAD, 0);
    if Assigned(UrlHandle) then begin
      FillChar(Buffer, SizeOf(Buffer), 0);
      AssignFile(f, destFName);
      Rewrite(f,1);
      i:=0;
      form3.Gauge2.Maxvalue:=bytesread;
      repeat
        Result := Result + Buffer;
        FillChar(Buffer, SizeOf(Buffer), 0);
        InternetReadFile(UrlHandle, @Buffer, SizeOf(Buffer), BytesRead);
        i:=myFileSize(destFName);
        form3.Gauge2.Progress:=i;
        BlockWrite(f, Buffer, BytesRead);
        Application.ProcessMessages;
      until BytesRead = 0;
      CloseFile(f);
      InternetCloseHandle(UrlHandle);
    end;
  end;
end;

Code:

function DownloadFile(strUrlFile, strDestFile: string;
comLabel: TLabel = Nil;
comProgressBar: TProgressBar = Nil
): boolean;
var
  handleNet: HINTERNET;
  handleUrl: HINTERNET;
  arrchBuffer: Array[0..1024] Of Char;
  dwFileSize, dwReserved, dwBytesRead: dWord;
  intNumByte: Integer;
  strReadFile: String;
begin
  Result := false;
  try
    handleNet := InternetOpen(PChar(Application.Title), INTERNET_OPEN_TYPE_PRECONFIG, nil, nil, 0);
    if Assigned(handleNet) then
      begin
        handleUrl := InternetOpenUrl(handleNet, PChar(strUrlFile), nil, 0, INTERNET_FLAG_RELOAD, 0);
        if Assigned(handleUrl) then
          begin

           // koliko je velik fajl
           arrchBuffer := '';
           dwFileSize := SizeOf(arrchBuffer);
           dwReserved := 0;
           If HttpQueryInfo(handleUrl, HTTP_QUERY_CONTENT_LENGTH, @arrchBuffer, dwFileSize, dwReserved) Then
              dwFileSize := StrToIntDef(arrchBuffer, -1);

           if comLabel <> nil Then
             comLabel.Caption := '0 od 0 bytes';
           if comProgressBar <> nil then
             begin
               comProgressBar.Min:=0;
               comProgressBar.Max:=dwFileSize;
               comProgressBar.Position:=0;
             end;

           FillChar(arrchBuffer, SizeOf(arrchBuffer), 0);
             repeat
               FillChar(arrchBuffer, SizeOf(arrchBuffer), 0);
               InternetReadFile(handleUrl, @arrchBuffer, SizeOf(arrchBuffer), dwBytesRead);
               for intNumByte := 0 To dwBytesRead - 1 Do
                 strReadFile := Concat(strReadFile, arrchBuffer[intNumByte]);

               if comProgressBar <> nil then
                 comProgressBar.Position := Form1.ProgressBar1.Position + StrToInt(IntToStr(dwBytesRead));


               if comLabel <> nil then
               comLabel.Caption := FormatFloat('0,000', Length(strReadFile)) + ' od ' + FormatFloat('0,000', dwFileSize) + ' bytes';

               Application.ProcessMessages;
             until dwBytesRead = 0;


           If Length(strReadFile) > 0 Then
             begin
               If FileExists(strDestFile) Then
                 DeleteFile(PChar(strDestFile));

               with TFileStream.Create(strDestFile, fmCreate) Do
                 try
                   Write(strReadFile[1], Length(strReadFile));
                 finally
                   Free;
                 end;
               result := True;
             end
           else
             result := False;
          end;
      end;
  finally
    InternetCloseHandle(handleUrl);
    InternetCloseHandle(handleNet);
  end;
end;

Code:

unit Unit1;

interface

uses
  Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
  Dialogs, ExtActns, Wininet, ComCtrls, StdCtrls, AutoUpdate;

type
  TForm1 = class(TForm)
    AutoUpdate1: TAutoUpdate;
    ProgressBar1: TProgressBar;
    Button1: TButton;
    procedure AutoUpdate1DownLoadUpdateDataProgress(Sender: TAutoUpdate;
      Progress, ProgressMax: Cardinal; var Cancel: Boolean);
    procedure Button1Click(Sender: TObject);
  private
    { Private declarations }
  public
    { Public declarations }
  end;

var
  Form1: TForm1;
implementation

{$R *.dfm}

procedure TForm1.AutoUpdate1DownLoadUpdateDataProgress(Sender: TAutoUpdate;
  Progress, ProgressMax: Cardinal; var Cancel: Boolean);
begin
ProgressBar1.Max:=progressmax;
ProgressBar1.Position:=progress;
end;

procedure TForm1.Button1Click(Sender: TObject);
begin
AutoUpdate1.UpdateAddress:='http://users.cjb.net/netwalker/';
AutoUpdate1.UpdateDataFile:='chbook.ini';
AutoUpdate1.DownLoadUpdateData;
end;

end.

Code:

function DownloadFile(source, destination: string): boolean;
var
SourceFile, LocalFile: string;
begin
SourceFile := source;
LocalFile := destination;
if URLDownloadToFile(nil, PChar(SourceFile), PChar(LocalFile), 0, nil) = 0 then
  result := true
else
  result := false;
end;

Code:

if not DownloadFile('http://www.sajt.com/path/to/file.ext','c:\file.ext') then
  showmessage('Ne mogu da skinem fajl')
else
 uradinestosafajlom; // ;)
end;