From Halopedia, the Halo wiki
Biological reproduction is the process by which new, individual organisms are produced. Reproduction is a fundamental feature of all known life; each individual organism exists as the result of reproduction.
San'Shyuum are known to have both male and female genders, and give live birth. Their reproduction is a strictly controlled affair though, considering the extremely limited gene pool, and individuals with undesirable genomes are added to the Roll of Celibates and forbidden to produce offspring to prevent negative recessive traits from entering the San'Shyuum gene pool. This does not prevent them from engaging in intercourse, however, and concubines are kept by high-ranking Prophets for this purpose. Illegal reproduction can result in the death of the unwanted child and sterilization of the guilty parent, even for a Hierarch.
San'Shyuum tend to wrap their necks around each other as a form of sexual foreplay. Mken 'Scre'ah'ben and his spouse, Cresanda, twined their necks intimately as they discussed the Roll of Celibates. Despite Mken being on the roll, they agreed that they should produce offspring. Similar to humans, the couple were breathless while attempting to speak during an intimate moment. Mken and Cresanda then proceeded to mate.
Huragok are the most unusual members of the Covenant, particularly in terms of reproduction. They lack genders as understood by other species - instead, two or even three Huragok work in unison to create a child, born of equal parts of the parents, sharing some memories and personality traits. While not true biological reproduction, the Huragok being artificial in origin and relying in microscopic nano-machinery to create new individuals, it still results in the creation of a new life.
The only known facts about Unggoy reproductive habits are that there are indeed two genders, male and female, and that they reproduce prodigiously, bearing a huge number of progeny. Exactly what means the species uses is never elaborated upon.
Many Unggoy were deliberately bred as an army in a place called the Redoubt. A number of "thrall colonies" exist where Unggoy are also for battle. The Banished incorporated the most mentally unstable of these Unggoy to be used as suicide squads.
Due to the Yanme'e insectoid bodies and use of Queens and Hives, it can be assumed that there is a dominant class within Hives. Like Ants, it may be that Yanme'e Queens produce fertile and infertile descendants. The infertile descendants would be used as workers and soldiers, whilst the fertile Yanme'e would be used to create more hives and keep the Yanme'e species going.
The sexual habits of Lekgolo, and by an extension Mgalekgolo, are not referenced in any canon material, and thus most details are based upon assumptions. Despite them being aliens, their appearance is approximately worm-like and as such it is assumed that they reproduce in the same manner as worms, asexually. It is known that each Mgalekgolo is formed from a single colony splitting in two, their dorsal spikes being the remnants of the last connections between the two parts of the colony, but this is not true reproduction in a biological sense, instead being the separation of two consciousnesses from one.
Jiralhanae have not been elaborated on in detail regarding the sexual habits of the two differing genders, and as such most assumptions made about their reproductive cycle is made through their physical appearance. Jiralhanae bear a striking resemblance to mammals which, apart from monotremes, are viviparous, bearing live young. As such, they would likely have external reproductive organs, mate through external physical means, and give birth to live children.
The Flood reproduce similar to that of a fungus spreading spores. The carrier forms produce Pod infectors. Once a Carrier form reaches the end of its lifespan, it explodes, releasing the Pod infectors. These infectors go on to spread further flood infection, ultimately creating more Carrier forms to repeat the cycle. Furthermore, there are Flood hives that produce Flood blisters along its biomass walls. These blisters incubate new Flood life. They explode upon hatching, releasing more Pod infectors. The hives themselves also produce spores which helps spread infection.