Here is an alternative to the Blizzard Account with cd-key registering for downloading games. These steps will show you exactly how to get started online with Warcraft 3 with nothing in your hands.

1st, we need to download the game. You can download both Warcraft 3 RoC and TFT as iso files. Note that you need both RoC and TFT to play Wc3 TFT.
Click Here to download WcIII RoC
Click Here to download WcIII TFT

These files which are cd images are both in .iso format. You can either burn them to a cd directly using any cd-burning software such as Nero, either extract them using Winrar or load them to a virtual cd-image loader such as Daemon-Tools.

2nd, after burning, extracting or loading the .iso file, we can now proceed to the installation of Warcraft 3. The setup should appear automaticly if you loaded or burned the .iso files, if you extracted them, you'll have to run the installer manually. During installation, you will be prompted to input a cd-key. This is where you input the cd-key you bought from this website or your own cd-key if you have one. Note that you need, of course, to install Wc3 RoC before Wc3 TFT.

3rd, you need to download the last patch from blizzard. What is really interesting in that last patch is that they removed the CD check, so you won't need any CD to play the game.
Click Here to download WcIII RoC patch 1.22a
Click Here to download WcIII TFT patch 1.22a

4th, install the patch and you are ready to play online! GL and HF!