While you can use Battle.Net, private PVPGN servers, lan emulators like Lancraft or GArena to find online games this services may not fit your needs.
If not you can try GameRanger. Works like GArena, GameRangers allow you to find and host online games for many games including Warcraft 3.
GameRanger is a free download for Mac and PC that lets you play over 600 games and demos online with friends and opponents worldwide. GameRanger offers features like profiles, friends lists, instant messaging, in-game voice communication, and competitive ladders/rankings/ratings.
Here is how to get started with GameRanger to find or host Warcraft 3 or DotA games.
First download, install and register GameRanger http://www.gameranger.com/download/
GameRanger will detect all supported games that you have installed.
You can check all available servers for installed games with drop-down menu by selecting My Games.
To filter only Warcraft 3 and DotA games you need to create group. You can do this by selecting Create new group from drop-down menu. There you need to check Warcraft III: Defend of the acients, Warcraft III: Reign of Chaos and Warcraft III: The Frozen Throne.
This will only show Warcraft 3 and DotA games.
This setting can be also changed when game lobby is created.
Now you just need to wait for players and click Start button.