(15) So [Naomi] said, “See, your sister-in-law has returned to her people and her gods. Go follow your sister-in-law.” (16) But Ruth replied, “Do not urge me to leave you, to turn back and not follow you. For wherever you go, I will go; wherever you lodge, I will lodge; your people shall be my people, and your God my God. (17) Where you die, I will die, and there I will be buried. Thus and more may the LORD do to me if anything but death parts me from you.”

(6) The servant in charge of the reapers replied [to Boaz], “She is a Moabite girl who came back with Naomi from the country of Moab. ... (10) She prostrated herself with her face to the ground, and said to him, “Why are you so kind as to single me out, when I am a foreigner?”

No Ammonite or Moabite shall be admitted into the congregation of the LORD; none of their descendants, even in the tenth generation, shall ever be admitted into the congregation of the LORD... You shall not abhor an Egyptian, for you were a stranger in his land. Children born to them may be admitted into the congregation of the LORD in the third generation.

The Talmud reconstructs the original dialogue in which Naomi discusses conversion with: Naomi said to her: On Shabbat, it is prohibited for us to go beyond the Shabbat limit. Ruth responded: “Where you go, I shall go” (Ruth 1:16), and no further. Naomi said to her: It is forbidden for us to be alone together with a man with whom it is forbidden to engage in relations. Ruth responded: “Where you lodge, I shall lodge” (Ruth 1:16), and in the same manner.

Naomi said to her: We are commanded to observe six hundred and thirteen mitzvot. Ruth responded: “Your people are my people” (Ruth 1:16). Naomi said to her: Idolatrous worship is forbidden to us. Ruth responded: “Your God is my God” (Ruth 1:16). Naomi said to her: Four types of capital punishment were handed over to a court with which to punish those who transgress the mitzvot. Ruth responded: “Where you die, I shall die” (Ruth 1:17). Naomi said to her: Two burial grounds were handed over to the court, one for those executed for more severe crimes and another for those executed for less severe crimes. Ruth responded: “And there I shall be buried” (Ruth 1:17).

Immediately following this dialogue, the verse states: “And when she saw that she was steadfastly minded she left off speaking with her” (Ruth 1:18). Once Naomi saw Ruth’s resolve to convert, she desisted from her attempts to dissuade her.

The Sages taught: When a convert who comes to convert, at the present time, They say to him: What did you see that you come to convert? Don’t you know that the Jewish people at the present time are anguished, suppressed, despised, and harassed, and hardships are visited upon them??

If he says: I know, and I [still feel] unworthy, they accept him immediately.

And they inform him of some of the lenient mitzvot, and of some of the stringent mitzvot, and they inform him of the sin [of neglecting the mitzvah to allow the poor to take] gleanings, forgotten sheaves, and produce in the corner of one’s field, and about the tithe to the poor.

And they inform him about the punishment for transgressing the mitzvot, and equally, they inform him about the reward for fulfilling them. ... And they do not overwhelm him, and they are not exacting with him [with details].

If he accepts, he's circumcise him immediately. ...When he is healed, they immerse him immediately, and two Torah scholars stand nearby and inform him of some of the lenient mitzvot and some of the stringent mitzvot. Once he has immersed and emerged, he is as a Jew in every sense.

(JPS translation:) (33) When a stranger resides with you in your land, you shall not wrong him. (34) The stranger who resides with you shall be to you as one of your citizens; you shall love him as yourself, for you were strangers in the land of Egypt: I am the LORD am your God.

Artscroll [Stone] translation:

When a proselyte dwells among you in your land, do not taunt him. The proselyte who dwells with you shall be like a native among you, and you shall love him like yourself., for you were aliens in the land of Egypt- I am HASHEM, your God.