How to install IntelliJ on Linux (Mint 13)

First it's highly recommended to use Oracle JDK instead of Open JDK because of incompatibilities

In your terminal

sudo add-apt-repository ppa:webupd8team/java
sudo apt-get update
sudo apt-get install oracle-java7-installer

Check with java -version that you get something like

java version "1.7.0_11"
Java(TM) SE Runtime Environment (build 1.7.0_11-b21)
Java HotSpot(TM) 64-Bit Server VM (build 23.6-b04, mixed mode)

If not try

sudo update-java-alternatives -s java-7-oracle

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Then download Intellij IDEA here
Extract then open idea-IC-123.94/bin/idea.sh with a text editor and add the following on the second line :

export IDEA_JDK=/path/to/java-7-oracle

(should be something like /usr/lib/jvm/java-7-oracle)

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If you try to launch idea.sh it should be good, now let's make a nice menu item

In Mint menu -> Control Centre -> Main Menu -> Programming -> New item
Name: IntelliJ IDEA
Command: /path/to/idea/bin/idea.sh
Description: Java IDE from JetBrains

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Time to download Android SDK

Extract it, go to /sdk/tools and launch "android".
Check what you want, I personnaly checked Tools, Android 4.2 (latest version), Android 2.3.3 (to test on "old" platform) and the Support Library under Extras.
Install X packages -> Accept All -> wait (better with a beer)

Run Intellij -> create new project -> Project SDK -> New... -> path/to/android/sdk

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Enjoy! ;)