Download and extract the MongoDB distribution for your system.
By default MongoDB will store data in /data/db/ which means you need to create and set the properties for that folder. You can use any other location if you'd like just remember to give the server the --dbpath option.
Run the server in a terminal window or use whatever means necessary to start the server process: ./<mongodb_location>/bin/mongod.
You can test whether it works by running ./<mongodb_location>/bin/mongo.
For more information read the manual.