The first jotun (giant) did not need a partner to procreate. He simply started sweating during his naps, and the droplets of sweat turned into his children, the jötnar (giants).
Odin, Vili, and Ve killed Ymir in his sleep. They used the different parts of his body to create the universe. The blood that poured from his wounds caused nearly all of his children to drown. One couple survived and fled to Jotunheim, where they would continue the giant race.