My question is that why different qults have different views about divorce. What is right way of divorce accourding to islam and tell also about the rite of halala where this exist for a common person which openion one should chose.
As the above excerpts from the Holy Qur'an indicate, a divorce (i.e., the talaq) is immediately followed by the waiting period (i.e., the iddat), during which time the husband has the right to revoke the divorce and take his wife back. However, this process can only be done twice; the third divorce is considered permanent no matter what.
At the end of the waiting period, the couple must choose either to reconcile or to make their divorce permanent. This decision is to be witnessed so there is no question as to the resolution. There is some question as to whether the original talaq needs to be witnessed as well, but without any evidences to mandate it witnesses shouldn't be considered a requirement.
After the divorce is rendered permanent, the couple are explicitly forbidden from remarrying each other until the woman marries (and subsequently divorces) another husband. The rite of halala, a form of temporary marriage wherein a man marries and divorces a woman only to make her lawful to her ex-husband, is to be avoided; according to the following hadith, such marriages are clearly against the sunnah of the prophet:
There is also some dispute whether the three divorces can be performed all at once (i.e., the triple-talaq), which would instantly make the divorce irrevokable. The crux of this dispute can be found in the following hadith:
While there are scholars who follow the example set by Umar (treating the triple-talaq as irrevokable), the prevalent opinion is that triple-talaq should be treated as a single talaq, as that was the sunnah of the prophet. In this case, a second or third talaq would only be counted after the wife had been taken back from the previous iddat.