"Anyone can be enlightened"

Self effort and meditation to achieve enlightenment are not universal in Buddhism. In Pure Land schools of Buddhism one has a relationship with Amida/Amitabha Buddha whereby one calls their name or chants homage to their name. Such a believer would aspire to be reborn in the Pure Land where one can much more easily become enlightened as one would then be hearing the Dharma directly from Amitabha Buddha. More information on Amitabha.

Anybody has the ability to become enlightened however different parts of Buddhism have different beliefs on how this happens. Everybody already has the seed of Buddha hood/ Nivada inside them which is hidden in till revealed in sincere practice. As long as the person is committed to becoming enlightened they have the ability to do so. Animals are the only exception to this rule as they need to create good Kama to enter the human realm before haveing the ability of enlightenment. People of higher realmes have to exercise restraint to avoid becoming attached to impermanent objects which cause Dukka (dissatisfaction) to exit the cycle of death and rebirth known as samsara. While this is the case in Zen Buddhism pure land Buddhism believes that you must have a relationship with Amitabha Buddha whereby one must call their name or chant homage. Pure land believers then hope to be reborn in samsara in the pure land were it is easier to stain enlightenment.

This is my understanding which is have understood from my GCSE course however it may not all be correct.

It is my understanding from reading Dogen that everyone already has Nirvana within them and it is hidden by a mask and revealed through sincere practice http://www.tricycle.com/web-exclusive/fundamentals-dogens-thoughts?page=0,1

Dogen says, “Between aspiration, practice, enlightenment, and nirvana, there is not a moment’s gap.” Thus, nirvana is one of the four elements in a practitioner’s spiritual activity. For Dogen, nirvana is inseparable from enlightenment, and it is inseparable from one’s practice at each moment. In other words, there is no authentic practice that lacks enlightenment or nirvana.

While Dogen discusses aspiration, practice, and enlightenment in detail, he does not explain the last element, nirvana, which seems to be an invisible element in his teaching. It is as though he talks about the experience of nirvana without using this word.

Nirvana is regarded as the realm of nonduality, where there is no distinction between large and small, long and short, right and wrong, appearing and disappearing, self and other. It may be called reality itself, or the absolute place beyond time and space. This is a realm that cannot be grasped objectively. The intuitive awareness or transcendental wisdom that goes beyond dualistic, analytical thinking and leads us into this realm is called prajna in Sanskrit.

Dogen calls this place of inner freedom the buddha realm. It is where one is many, part is whole, a moment is timeless, and mortality is immortality. To experience this beyondness in the midst of the passage of time, change, and decay is a miracle. For Dogen, this miracle can happen each moment, as each moment of duality is inseparable from a moment of nonduality.

Dogen is generally considered to be a Zen practitioner, but how can we exclude his observations from his own experience from any Buddhist practice?

Here is another source that reinforces the ever present Nirvana in each of us http://bdtest1.squarespace.com/web-archive/2010/9/9/moment-by-moment-nirvana.html

It is not that duality stops existing or functioning; the small is still small and the large is still large. The body remains the body and the mind remains the mind. Without discerning the differences between things, we could not conduct even the simplest task of our daily lives. And yet, in meditation the distinctions seem to dissolve and lose their usual significance. Dogen calls this kind of nondualistic experience nirvana, which exists at each moment of meditation.

There are so many areas of Buddhism and sects and circles within each sect that to find a universal belief in every sect of Buddhism is doubtful. My primary concern is does the primary area of my practice hold this to be true, or if nothing else do I hold this to be true. My own practice confirms to whatever degree possible what Dogen says from his ultimate experience.