Here is a quote from the Douay-Rheims edition of the Bible. From the Gospel of Saint Mark, Chapter 10.
"And rising up from thence, he cometh into the coasts of Judea beyond the Jordan: and the multitudes flock to him again. And as he was accustomed, he taught them again.  And the Pharisees coming to him asked him: Is it lawful for a man to put away his wife? tempting him.  But he answering, saith to them: What did Moses command you?  Who said: Moses permitted to write a bill of divorce, and to put her away.  To whom Jesus answering, said: Because of the hardness of your heart he wrote you that precept.
 But from the beginning of the creation, God made them male and female.  For this cause a man shall leave his father and mother; and shall cleave to his wife.  And they two shall be in one flesh. Therefore now they are not two, but one flesh.  What therefore God hath joined together, let not man put asunder.  And in the house again his disciples asked him concerning the same thing.
 And he saith to them: Whosoever shall put away his wife and marry another, committeth adultery against her.  And if the wife shall put away her husband, and be married to another, she committeth adultery."
Anyone who is in a state of mortal sin should not take communion. Adultery is a mortal sin. Divorcing one’s first spouse and becoming remarried was defined by Christ Himself as adultery. Therefore, as long as the remarried partners remain in that relationship and have sex, they are committing adultery against their actual (first) husband or wife and are thus barred from Communion until they either break up or begin living together as brother and sister (get separate bedrooms, you get the idea) and go to Confession. However, if you are divorced and chaste then you can go to Communion, since then you are not committing adultery against your spouse.
To the best of my belief (others, please correct me if I am wrong) if you were divorced **before **you were baptized/confirmed in the Church and your marriage was not performed in the Church, then the Church does not consider it a real, sacramental, unbreakable marriage. You can get married validly in the Church in such a case or go to Communion.