In Starcraft 2 all the published maps on Battle.net is up and ready to be played, the maps are on the actual server.
So if you want to download new Multi-player maps you first go to the Multi-player menu.
Then just click at CREATE A GAME in the Multi-player menu.
Then they have a box which says "Search by name". Enter the map name you want to download and/or host in that search box and then the list will update and give you the map you searched for.
Click on the map in the list below and then click CREATE GAME. Now you will download the map and host it.
In tournaments you no longer will download like a map pool .zip file and put it in your maps folder, in the age of Starcraft 2 you will find all the maps you want by simply searching its name.
When publishing a map to the server it will only publish it to 1 realm. So if you log in on an account in the editor with EU key and publish a map, the map can only be found in the EU server. Also remember that you will only find the map by search if it's hosted as Public, private maps can only be downloaded through friend invite and can only be hosted if you already have the map.
This tutorial was made to enlighten people and tournament admins on how you use the new map system in Starcraft 2. I will link my maps to this thread and feel free to do the same with your maps