I think this is what you want. Run the following command in Terminal.
sudo apt-get install openjdk-7-jre
When you're searching for a program like this, try the following command:
apt-cache search keywords here
So for instance,
apt-cache search jre 7
icedtea-7-jre-jamvm - Alternative JVM for OpenJDK, using JamVM
openjdk-7-jre - OpenJDK Java runtime, using Hotspot JIT
openjdk-7-jre-headless - OpenJDK Java runtime, using Hotspot JIT (headless)
openjdk-7-jre-lib - OpenJDK Java runtime (architecture independent libraries)
openjdk-7-jre-zero - Alternative JVM for OpenJDK, using Zero/Shark
You may then use common sense to figure out which package to install.