The Almighty God describes a valid divorce by men (talaq) as follows in the Surah At-Talaq:
“O Prophet, when you [Muslims] pronounce the words of divorce to women, divorce them by regarding their waiting period and keep count of the waiting period, and fear Allah, your Lord. Do not turn them out of their [husbands’] houses, nor should they [themselves] leave [during that period] unless they are committing a clear immorality. And those are the limits [set by] Allah. And whoever oversteps the bounds set by Allah has certainly wronged himself. You know not; perhaps Allah will bring about after that a [different] matter.
And when they have fulfilled their term, either retain them according to acceptable terms (maruf)  or part with them according to acceptable terms. And bring to witness two just persons from among you and establish the testimony for [the acceptance of] Allah. That is instructed to whoever should believe in Allah and the Last day. And whoever fears Allah – He will make for him a way out.
And will provide for him from where he does not expect. And whoever relies upon Allah – then He is sufficient for him. Indeed, Allah will accomplish His purpose. Allah has already set for everything a [decreed] extent.” (At-Talaq/ The Divorce 65:1-3)
The waiting period is three CLEAN periods for the women having regular periods , three months for women having irregular periods, and until the birth for the pregnant.
The divorce words MUST be pronounced
1- While the woman is NOT on her menstruation period AND
2- In that clean period of the woman, the spouses MUST NOT have had intercourse.
Only then, counting the waiting period may begin.
When the man does not send his wife away from the house during the iddah, the couple may have convenient time and atmosphere to resolve the disputes between them. The woman who does not leave the house can get the chance to convince her husband to the continuation of marriage. Neglecting these would make reconciliation difficult. However, the talaq would still be valid if any of these cases occur, because the verse says: “whoever oversteps the bounds set by Allah has certainly wronged himself“.
The man must count the period.
3- If the man returns to his wife within the waiting period, this return must be approved in the presence of two witnesses. Then, they can come together without needing a new nikah.
If the man does not return within the iddah, the divorce must be approved in the presence of two witnesses.
Marriage is finalized in case of a divorce as described in these verses.
You may have further information in our following articles:
Divorce by women is called “iftidaa” and it is explained in the following post: