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.
