Most well-known Saints have been officially moved into Sainthood by the Roman Catholic church, which has a very long and complicated process of declaring someone a Saint. One of the first steps is called Beatification; one of the last steps is Veneration. Jews have a more hesitant approach to Sainthood. Generally, they believe in becoming better persons. They also insist that the most noble person cannot be a Saint if they are ignorant of the Bible and the Talmud. Then again, the Kabbalist declares: "The goal of the Mystic is to establish devekut, union with, or, as Jewish mystics prefer to define it, cleaving to God."
(The Kabbalah Institute of the Galilee: Mysticism Collection)

To me, Saints are persons who are able to be in direct contact with Pure Awareness (God) at least in moments of intense concentration. Of course, any contact with God can never be like the meeting between two persons. God is not a person. God and the Self can only be understood as omnipresent Awareness.

But what of the other qualities normally associated with Sainthood?
If one considers miracles alone, any psychic power observed from time to time in regular people may suggest Sainthood, although these individuals might not in any other way be saintly. And the Halos depicted in older paintings are probably best sorted in under artistic expression. On the other hand, we now know that all matter radiates. Therefore it is entirely possible that someone was able to recognize the stronger radiation eminating from individuals in direct contact with God. Here it might be interesting to point out the medical mystery of synesthesia. People who have this "disorder" might feel shapes, hear light, see sound and so on.

The strongest argument for declaring someone a Saint must remain direct knowledge of God. Everything else comes second and there are many passages in the Bible which clearly support this view.
Since knowledge of God is the key ingredient of Sainthood, I do not see any difference between a Saint who knows God and a Mystic who knows God.

How do Saints and Mystics become One with God?

Through intense Concentration, and by following the first and most important commandment:
"You shall love God with all your heart, mind and soul."

God's Pure Beingness is experienced when the mind quits thinking because our Soul is also pure Awareness when there is no thinking. Our Soul is the part which is made in His image. That is why the Bible says in Psalm 46:10 "BE STILL and recognize that I AM GOD."
Or, in Psalm 4:4 "Commune with your own Heart..., and BE STILL."

Likewise we read in the Bhagavad Gita 6:27 "Supreme Bliss comes to the seeker whose mind is Completely Tranquil and whose passions are Quieted, who is free from stain (any thought) and who has become ONE with God."

Related article: Spiritual Growth

Note: If you are going to try this, be advised that most struggle for many years to achieve perfect concentration or perfect devotion.