What is the perspective of a non-believer in Islam?

The general concept of a "non-believer" has been widely misunderstood, particularly in the Islamic world.

The main concept here is that Islam concentrates on belief rather than cultural influences or traditional rituals. This is why nationality and background are completely irrelevant to a Muslim. Only 18% of the 1.6 billion Muslims of the world are Arabs. There is no inherit privilege to a Muslim just because they are Arab. It is merely that the Quran was revealed to an Arab prophet much like some of the previous scriptures were revealed to Hebrews. There is no "birth-right", and no preference towards one human being and another.

The only measure in Islam is faith.

Even to become a Muslim, it is merely a declaration of faith to acknowledge your belief in God, rather than to perform any special rituals.
To "submit" then, is the acknowledgement of the truth of God's existence, so you could say that the word "Muslim" is actually a descriptive noun... one who submits to the notion of the existence of God.

Further to this believe, is one's acknowledgement of the afterlife, that God created an eternal sanctuary after the trials of this life are done. Many non-believers ask why they will not be amongst those who enter this eternal sanctuary, but that question is in itself an oxymoron.
If one doesn't believe in God, that would imply he doesn't believe in the afterlife either, so why would it concern him to contemplate not entering a realm he does not believe exists in the first place?
Would it not make sense that if God created an afterlife, that at least the only requirement would be belief in His existence? Again I will emphasize that this requirement is not based on a "birth right" or an ethnicity or an attribution to one group or another, but rather the very simple concept of belief that He exists. In fact there is a Hadith that describes the requirement of this belief as "No one who has an atom’s weight of faith in his heart will enter Hell eternally". So it is a pretty simple requirement.

Moreover, just because I believe today, and you do not, does not mean that I am exempt or more "privileged" than you are in this regard. Quite the contrary.

We are still equal in the eyes of God because my last dying breath may be void of faith, and you may live your life with the eventual realization that God does indeed exist. You may grow to be much more pious than I ever was. Your belief may not even be realized by anyone. This is precisely why mankind is not entrusted as being the judges of faith, but rather the ones to be judged. It is God and God alone that has the right to determine ones true faith, especially when many could be impostors of the faith, only to pretend to believe just to receive acknowledgement from their Muslim peers.

The complexity of each and every one's personal circumstances also plays a big part in God's Mercy. A tribal African boy who has never had exposure to the teachings of the One True God, may be exempt from judgement of faith simply because the opportunity never found its way into his isolated life. A mentally disabled person also has his own circumstances, and so on...

The world is too complex for any one mere man to proclaim judgement of another man's faith, regardless of the systems we have in place to say otherwise. And for that reason alone, I can never say that you are a "kafir" and can never truly determine that you will not be of those who enter paradise to be in the company and Grace of the Almighty.

How easy is it for a Christian to become a Muslim?

The best way to describe Islam relative to Christianity is by considering their holy scriptures. With regards to the "Old Testament" and "New Testament", you can consider the Quran to be the "Last Testament".

Islam is part of the progression of Abrahamic faiths and for that it acknowledges the validity of Judaism and Christianity respectively as part of its affirmation of truth.

It is the final and lasting message of God that sealed the teachings of the Messengers that have lived amongst us throughout mankind, including Abraham, Moses, Jesus, Noah, and many more.

For that very reason it is quite easy for a Christian to become Muslim as part of his progression of faith.

There was once a person I heard say that they wanted to become a better Christian, and decided to become a Muslim for it.

Our love for the beloved Jesus Christ is one that can appeal to anyone coming from Christianity. We acknowledge his piety, his devotion and his sacrifice; we believe in his miraculous birth, and his ascension to heaven before his death, we believe in the miracles bestowed upon him which gave him the power to heal the leper, cure the blind, and raise Lazarus from death. We hold his mother Mary amongst the most highly regarded females in the history of mankind.

His message is consistent with that of Moses's and Abraham's, which makes sense that we regard him in the same way as those who preceded him with the same rallying cries.

Muslims believe in the Gospel of Jesus, or more precisely the word of Jesus as the message of God, which is why we do not acknowledge the validity of scriptures written by people of the faith such as Matthew, Mark, Luke and John. Though they may be pious saints with good intentions, their scripture can only ever provide support to a faith rather than become the backbone of the faith, much like Hadiths are accounts of the Prophet Muhammad during his lifetime by many who lived amongst him.

The Quran, however, is the word of God directly relayed to mankind by an illiterate man who would have been incapable of "making it up" due to its comprehensive explanations of all aspects of humanity including spirituality, governance and details of the world around us. Subsequently these words were written down by his companions in order to preserve the message.
It has been unaltered and uncompromised since the revelations occurred which is why we hold the authenticity of Islam with high regard.

Even the original scholars of Christianity realized that their scripture was incomplete purely based on the manuscripts they had, which is why they adopted the Old Testament to create a complete Bible. It would have made more sense to consider the "Last Testament" instead.

We do not celebrate Christmas because that is technically not part of Christianity since the birth of Christ is actually unconfirmed and the date that was chosen was more in line with the celebrations that pagans had during that time of the year.

Considering all this, a Christian would not have to forgo his faith, but rather continue it through Islam for a more complete picture of the entire message.

The "how" is the easiest part. There is no official ritual required to become Muslim because it stays true to the concept of a belief system not a cultural movement, and so one's mindset is really what counts.
All that is required is a simple proclamation of faith.

Since the next Messenger to follow Jesus in succession was the Prophet Muhammad, the proclamation would require an acknowledgement that he indeed is also a contributor to the message of God, as Jesus was.
Therefore the following statement is all that is needed to be a Muslim:

"La Ilaha Illallah, Muhammad rasululah"
"There is no Lord but God alone, and Muhammad is His Messenger"

And done... you become Muslim.