I downloaded zeppelin 0.5.6 (http://www.apache.org/dyn/closer.cgi/incubator/zeppelin/0.5.6-incubating/zeppelin-0.5.6-incubating.tgz), extracted, and started zeppelin-daemon.sh.
localhost:8080 shows the zeppelin interface, but nothing is working. it looks like the interpreters are not defined properly.
shift+enter on the cells just return the cell context, even when trying sc.appName or sc.master to see SparkContext configuration.
The documentation specify that spark should be available without any config., and I couldn't find the required configuration to enable spark (export SPARK_HOME in bin/zeppelin-env.sh didn't help either).
It would be good to know what you have in logs/ folder. Also in the right corner is a button indicating if your are "connected" or not, either green or red. To check the interpreters please open the Interpreter tab, what happens if you restart Spark? What is in the logs? By default the Spark interpreter is executed as local[*], so running as a local process, that is why it should work out of the box. In zepplin-env.sh it might also be worth to set JAVA_HOME.