To start with MongoDB database you need to download and install the MongoDB database. It is available in two flavors.
1. MongoDB Enterprise
2. MongoDB
MongoDB Enterprise is a commercial edition of MongoDB. The current production version for MongoDB Enterprise edition can be downloaded from https://www.mongodb.com/products/downloads/mongodb-enterprise
MongoDB is available for different platforms and version. Depending upon your requirement you can download the MongoDB for Windows, Linux, Mac OS X and Solaris platform. There is 32-bit and 64-bit version of MongoDB available. The current production version available for MongoDB is 2.4.9. You can download the MongoDB from http://www.mongodb.org/downloads
To learn MongoDB you can download the Non-enterprise edition of MongoDB.
To learn how to install and configure the MongoDB on Windows, you can follow this excellent video available on youtube.
http://www.youtube.com/watch?v=QcP4XExUpfA
If you are not interested to download and install MongoDB or you cannot do it on your machine due to any reason, you can go to http://try.mongodb.org/ and start learning MongoDB online. This online source is a great place to start learning MongoDB without installing it.