Can a woman who was divorced by her first husband (he left her and married again) receive Holy Communion?
Yes. If a divorced person has willfully destroyed a valid marriage, or if that person has entered into another romantic relationship, that person is barred from Communion until he has regularized his status in the Church through confession and/or an annulment. As neither of these circumstances apply in this case, the person is able to receive Communion, assuming she is otherwise in a state of grace.
The Catechism of the Catholic Church states:
It can happen that one of the spouses is the innocent victim of a divorce decreed by civil law; this spouse therefore has not contravened the moral law. There is a considerable difference between a spouse who has sincerely tried to be faithful to the sacrament of marriage and is unjustly abandoned and one who through his own grave fault destroys a canonically valid marriage. (CCC 2386)
The Congregation for the Doctrine of the Faith, in Concerning the Reception of Holy Communion by the Divorced and Remarried, has said that a divorced Catholic who has not remarried can receive Holy Communion after receiving the sacrament of confession and living in complete continence.