A man who wishes to wed a woman can do so in one of three ways: money, a contract, or sexual relations.
For intercourse, one must have two witnesses who see the couple isolating themselves. The man must say to the woman “You are set aside for me by this intercourse according to the laws of Moses and Israel.” Afterwards he must have intercourse with her.
The scholars asked: For purposes of marriage through intercourse, is it sufficient for the glans of the penis to penetrate, or does he have to fully penetrate her? This question is important, the scholars added, in case a man marries a woman through intercourse and has time only to penetrate her with his glans before another man marries her through money. The question is: to whom is the woman married? If we suppose that penetration with the glans is enough, she is married to the first man; if we suppose that one must fully penetrate to effect a marriage, she is wed to the second man. (The Talmud rules that there must be full penetration for marriage by sexual intercourse, because a man who marries a woman by sexual intercourse intends to have full penetration.)
(Babylonian Talmud, Tractate Kiddushin 10a)

The Talmudic text:
They asked: Does the start of sexual intercourse acquire her, or the end of sexual intercourse? What is the practical implication? A man began to have sexual intercourse with a woman and during the intercourse she stretched out her hand and accepted engagement money from another man, or in the case of a High Priest who marries a virgin through intercourse [if he does not acquire her until the end of relations, she is no longer a virgin, and she is forbidden to him]. Ameimar, quoting Rava, stated: Anyone who has sexual intercourse intends full penetration.