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
Explain that in the temple, through the power of the priesthood, Chris and her husband could be married for eternity, not just until death. Their children would then be “born in the covenant,” which means that they could be sealed together as a family forever.
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:
Can you expand on the case where one woman would marry multiple men, because of death? Since she was married to multiple men, whose wife in the afterlife is she?
The woman would be the wife of the earliest celestially worthy husband.
Also, if there happen to be more men than women in the highest degree of glory, would a woman have multiple husbands?
No. There would be men who don't have celestial wives.