If you are using Intellij 14 or later you need to add the following to the end of your build.gradle before importing:

idea { module { inheritOutputDirs = true } }

If you don't do that, your assets will not work. (Thanks to SanAndreasP for finding this solution)


All that is left to do are the run configurations, so that you can actually start Minecraft. For those again open the Gradle sidebar and run the
genIntellijRuns
task. Intellij will now ask to reload the project, click OK.

In most recent versions of IntelliJ you now have to go into Run > Edit Configurations and adjust both run configurations to say Use Classpath of Module _main.