This is long before the days of IVF, cloning, artificial insemination and test tube babies... ok maybe not test tube babies.. but the problems faced by many childless parents in the Mahabharat is the same faced now... only the way the story is packaged is really interesting. So if Kunti goes and asks a sage "how to make kids?" the sage gives her a "mantra" instead of explaining the ins and outs of the standard procedure. This way, you can tell the story to little kids.
A sage who indulges in meditation, or tapas, explores the universe through the inner eye and has no care or concern for the "real" world. This was an idea that a sage called Vishwamitra took to heart, and no worldly pleasures could distract him from his tapasya. Now the king of the Gods, Indra, felt a little insecure and tempted Vishwamitra with many heavenly beauties and suchlike. They were all unsuccessful till Menaka managed to seduce him and bore him a son - Dushyanta. Vishwamitra said the whole affair was a ploy, and pretended he had nothing to do with his son, who was orphaned and brought up in a hermitage. He grew up to marry Shakuntala, and the story of India begins with their son, Bharat. Bharat was a little unlucky, the sages then had not progressed in their tapas enough to help him out, or he did not seek divine help; either way, he did not have a son to hand over his kingdom to. It is unclear that if he ever had a wife, but even if he did, women in those days were considered non living things if they could not conceive. Bharat did a bright thing, went right ahead and held the first general elections in India, and established India as a democracy. The elected "king" was Shantanu. Shantanu had his own share of problems in the child-bearing department. Conception was not a problem, but the problem was his wife, who killed every child he got. He protested when she was about to do this for the seventh time, and Bhishma was allowed to live, while his wife, Ganga, left him. The story may be similar to that of Krishna, only he was the eighth. Shantanu, now single, fell for the charms of Satyavati, a fisherman's daughter while out on a hunting expedition. Satyavati agreed to marry him as long as her son got to be the king instead of Bhishma, and Bhishma, being the good son that he was, took an oath never to marry so that his father could have a wife. Out of their union were born Chitrangadha and Vichitravirya. Bhishma, being the good half-brother that he was, took up the responsibility of getting the two married, and kidnapped three wives for them, Amba, Ambika and Ambalika. Amba wanted to marry Bhishma, because, after all, he had won her over. Bhishma told her of his promise, she yelled at him for ruining her chances of getting a good groom, and went her way. The remaining two settled down with Bhishma's half-brothers but both the half-brothers died before they made babies. Enter the sage Vyasa, who begets children with their wives by virtue of being a sage. Dritarashtra and Pandu, are born as the official sons of Chitrangadha and Vichitravirya, are the heirs to the throne, but are fathered by Vyasa. Enter Kunti, a little girl who gets celestial sex education and through "means unknown" conceives Karna, get's shit scared, lets the baby float down a river and for all practical purposes, retains her virginity. Then she gets married to Pandu, and conceives three more children for him - that aren't really his. Dharmaraja is Yama's son, Arjun is Indra's son, Bhima is Vayu's son. How Kunti manages this is anyone's guess, but little kiddies in India are told that she does this using a mantra. She teaches the 'mantra' to Pandu's second wife, Madri, who also, through means unknown conceives Nakul and Sahadev who are the children of lesser Gods in the hevenly hierarchy. Dritarashtra, and his wife Gandhari, meanwhile have birth complications of their own. Vyasa, who has progressed the field of genetics since the days of Bharat, puts their fertilized embryos in pots, and conceives a hundred children for them. That is the beginning for the mahabharat, and a catalogue of how to beget.