In order to play Custom levels, you need a beta version of the Dolphin emulator and an SMG2 iso.

First step: Download the custom level you want to play. You can find them in the resources tab.

After downloading them, you should have a .rar file. Extract the file. You now have a folder with an XML Riivolution archive.

Open Dolphin. Right-click on Super Mario Galaxy 2. Select 'Start with Riivolution Patches' then click on 'Open Riivolution XML'.

Go to your Riivolution folder and select the XML file

Just make sure you enable it and you should be good. The custom level will appear on the map just like the other levels so you'll probably have to search through the map in order to play it.