‘Iddah After Divorce
Question

I hope that you can explain the ‘Iddah of a woman divorced by Talaq.
Praise be to Allah.‘Iddah after divorce
If the woman is divorced by talaq before the man has entered upon her and been alone with her, i.e., before intercourse or intimacy with her, then she does not have to observe any ‘Iddah at all. Simply by virtue of the divorce it becomes permissible for her to marry another man. 
But if he has entered upon her and been alone with her and had intercourse with her, then she has to observe the ‘Iddah (waiting period) which takes one of the following forms:
Forms of ‘Iddah after divorce 

If she is pregnant then her ‘Iddah lasts until the pregnancy ends and she delivers, whether that is a long time or a short one. It may so happen that he divorces her in the morning and she gives birth at noon, in which case her ‘Iddah is over. Or it may be that he divorces her in Muharram and she does not give birth until Dhul-Hijjah, so she remains in ‘Iddah for twelve months. The point is that the ‘Iddah of the pregnant woman lasts until she gives birth, no matter what the case, because Allah says (interpretation of the meaning): 

“And for those who are pregnant (whether they are divorced or their husbands are dead), their ‘Iddah (prescribed period) is until they lay down their burden.” [At-Talaq 65:4]

If the woman is not pregnant and she menstruates (is of child-bearing age), then her ‘Iddah is three complete menstrual cycles after the divorce, i.e., her period comes then she becomes pure, then her period comes again and she becomes pure, then her period comes again and she becomes pure. That is three complete menstrual cycles, regardless of whether the time between them is long or short. Based on this, if he divorces her and she is breastfeeding and does not menstruate until two years later, then she remains in ‘Iddah until she has had three menstrual cycles, so she may stay in this state for two years or more. The point is that she should go through three complete menstrual cycles whether the time involved is long or short, because Allah says (interpretation of the meaning): 

“And divorced women shall wait (as regards their marriage) for three menstrual periods.” [al-Baqarah 2:228]

If a woman does not menstruate, either because she is very young or old and past menopause, then her ‘Iddah is three months, because Allah says (interpretation of the meaning): 

“And those who no longer expect menstruation among your women - if you doubt, then their period is three months, and [also for] those who have not menstruated.” [At-Talaq 65:4]

If a woman’s periods have ceased for a known reason and she will not menstruate again, such as if her uterus has been removed (hysterectomy), then she is like one who has passed menopause and her ‘Iddah is three months. 
If her periods have ceased and she knows the cause, she should wait for the cause to cease and for her periods to return, then she should observe ‘Iddah according to her menstrual cycle. 
If her periods have ceased and she doesn't know what caused that, then the scholars say that she should observe an ‘Iddah of a full year, nine months for pregnancy and three months for ‘Iddah. 

These are the categories of ‘Iddah for women divorced by Talaq. 
For more about ‘Iddah issues, please see these answers: 145 , 127974 , 101546 and 311 .
And Allah knows best.