Simply put, Nirvana is achieved (achieve is a bad word. its more like realize) by understanding that the whole universe is an illusion created by the mind. The mind is also a part of the universe, so mind is also created by mind. When one understands that everything we see, feel, smell etc. are just illusions created by mind, he/she can detach from them, and attain a state where there is complete peace and calmness.
This is the very very basic, most core idea. The actual concepts are much more complicated than this, and require a lifetime of devotion and practice to fully realize.
To do this, one must follow the Eight Fold Path.