MongoDB is not an application but a service – it does not have a graphical interface by itself. It is used only through other applications, for storing and retrieving data; most commonly by web sites (diaspora*, Craigslist, for example).
When writing a program yourself, you would use a "driver" to connect to the database from whichever language you use. For example, in Python (interactive mode):
>>> import pymongo
>>> connection = pymongo.Connection("localhost")
>>> db = connection.testdatabase
There are applications for browsing the entire MongoDB contents; most of them are listed in the Admin UIs page at MongoDB website.