Using Indy's TIdHTTP
component:
var
Params: TStringList;
Data: string;
begin
Params := TStringList.Create;
try
Params.Add('UserName=' + UserName);
Params.Add('Password=' + Password);
Data := IdHTTP.Post('http://mypage.com/_LAYOUTS/com/Handlers/LoginHandler.ashx?task=Login', Params);
finally
Params.Free;
end;
end;