I've not seen/read any female Orcs mentioned in the movies or in the books. In one of the movies, an Uruk-hai is momentarily shown emerging from a giant, grown-Orc sized flesh packet. So are they created with spells, or do they follow the Standard Reproductive Model.
It's clearly stated multiple times in The Silmarillion that only Ilúvatar can create life.
In chapter 2 of "Quenta Silmarillion" ("Of Aulë and Yavanna"), Aulë creates the dwarves, but Ilúvatar chastises him:
Why dost thou attempt a thing which thou knowest is beyond thy power and thy authority?
In chapter 3 ("Of the Coming of the Elves and the Captivity of Melkor") the creation of the Orcs is explained:
...all those of the Quendi who came into the hands of Melkor, ere Utumno was broken, were put there in prison, and by slow arts of cruelty were corrupted and enslaved; and thus did Melkor breed the hideous race of the Orcs in envy and mockery of the Elves...
For the Orcs had life and multiplied after the manner of the Children of Ilúvatar; and naught that had life of its own, nor the semblance of life, could ever Melkor make...
The Munby Letter includes an authorial statement on this matter:
There must have been orc-women. But in stories that seldom if ever see the Orcs except as soldiers of armies in the service of the evil lords we naturally would not learn much about their lives.
There's also a caution in this statement - if Orcs (or any other being, for that matter) are only ever seen in one context within the story, then you don't need (and shouldn't feel that you need) any kind of explicit statement regarding their activities in other contexts.
Orcs originated from Elves, twisted and tainted by Morgoth. As the elves taken were both male and female, the first Orcs were also male and female. As such, they are able to reproduce.
I always imagined that Orcs can reproduce in two ways.
All Orcs either fill a male or female role in the reproductive cycle. All Orcs, however still appear and act masculine. This would also explain why Orcs never seem to hold any desire for women, because they probably have no concept of sexual preference.
Powerful magic-users such as Melkor, Sauron, or Saurman are capable of using some sort of device or substance to manufacture Orcs. Orcs' numbers seem to grow much faster when a powerful magic-user is leading them. The Orcs pretty much stopped breeding, and devolved into Goblins once The One Ring was destroyed and Sauron was defeated. My guess is that these Orcs were breeded, and thus didn't know how to reproduce sexually, or just couldn't supplement their numbers as they relied on Sauron's breeding.
I feel this would explain a lot. It was clearly very surprising when Saruman was able to mass such a large amount of Uruks so quickly, so I imagine magical breeding was involved. It would also explain the relationship between Azog and Bolg, since Bolg is Azog's son, and inherited his rank when Azog died. It's also said that Uruks were bred with Men, so they would need some form of sexual reproduction. So in essence, both of these methods of reproduction could exist at the same.