I have heard or read something that the LDS church teaches that there will be marriage and even polygamy in the after life for people who are good Mormons. Is this available for all people are just a few? And what are the specific teachings about this?
Preparing for Exaltation Teachers Manual - Lesson 41: Eternal Marriage
If you are married in an LDS temple, for time and all eternity, and you reach the highest of the three degrees of glory after death, the celestial kingdom, and your wife and children reach the celestial kingdom, your marriage and your family is yours forever.
So no, eternal marriage and family are not for everybody.
If a man marries more than one woman while on earth, because of the first wife's death, then he will be married to both women in the celestial kingdom.
Women who make it to the celestial kingdom because of their faithfulness, and whose husbands don't make it to the celestial kingdom, because of unfaithfulness, are eligible to marry a different, faithful husband in the celestial kingdom.
Edited to add answers to the questions in Narnian's comment:
The woman would be the wife of the earliest celestially worthy husband.
No. There would be men who don't have celestial wives.
In the instance of a woman being married to several husbands in this life, she can only be sealed or "Eternally married to one while living. Assuming all of the husbands were worthy she would have been sealed to the first,for eternity, and the others just for this life. Incidentally, there are more righteous women than men, so there will be fewer men available in the highest kingdom. Hope this helps, Peter.