check with either:
ps -edaf | grep mongo # "ps" flags may differ on your OS or
/etc/init.d/mongod status or
service mongod status to see if mongod is running (you need to be root to do this, or prefix everything with sudo)
check the log file /var/log/mongo/mongo.log to see if there are any problems reported.
For quickly checking if mongodb is running, this quick nc trick will let you know.
nc -zvv localhost 27017
The above command assumes that you are running it on the default port on localhost.