I will be as tasteful as possible, for my more... innocent followers. I will leave out the grisly details.
All of my kind have both organs, fully functioning. For highly advanced and evolved creatures, gender dimorphism does eventually go away entirely. Humans are not at that level yet, but there is some signs of this advancement among them that I have seen thus far. Gender is soon to become naught but a concern of the past, I think. Of course, the time scale we follow is quite different, so soon by my standards could be thousands of years by yours. While one of us may identify as either male or female... it’s really no big deal to us. I, for example, appear as and identify as male, but I do have fully functioning female parts as well.
Either way, we have the ability to both lay, and even incubate eggs, as well as fertilize them. My eggs, at least, are soft and jelly-like, and quite small, especially when compared to myself. I can choose to incubate them myself, but such is tiring on my resources so I much prefer a willing host.
Creating Spawn does not require a partner. I both provide the eggs... and fertilize them. This creates my Spawn, who are smaller and less powerful than I am, as they only get a small bit of my genetic material. They often look like me, though their color and body type can vary widely. While they can be just about any color, I find blues and greens are the most common.
Generally, I will choose a host. They can also be hidden away, but they take three times as long to incubate that way, and are at greater risk of being found and eaten by some ocean predator, or never hatching. Incubating them myself is also an option, but this does get rather tiresome after a time. I find humans make the best hosts, as they take half the time to incubate eggs as other sapient species.
In short, the host will take the eggs into their own womb, incubate them, then be drawn to water when they are close to hatching. Once they reach some water, the eggs will come back out and hatch. The hatchling Spawn are tiny compared to me, but they are drawn to follow me, even if they do tend to wander off due to their natural curiosity. A side effect of Sapience, you see, so I like to see them being curious and even helping each other and cooperating. I usually create between four and fifteen spawn per clutch, but the average is between six and twelve... depending on the host, of course. Stronger hosts can handle more eggs.
Spawn are unable to reproduce, and while they each have their own personality, they are instinctively drawn to me as their progenitor. They are not bound to my will, and are free to be who they want to be, but they know that I take care of them and watch over them. They do not have the power my kind have, and they grew much faster.
True reproduction, as in creating an offspring instead of a Spawn, is achieved quite similarly. Myself, or whoever I am breeding with, will place eggs into our own womb. They are, in fact, produced in a separate organ. Once there, they can be fertilized by our chosen mate. It’s useful, really. Any pregnancy has to be intentional, so if there are not the resources to raise a new offspring, there will be no new offspring.
When they are a true offspring, not just a spawn, we can only incubate one at a time. No matter how many eggs one starts with, only one will survive to hatching when they are an actual offspring.
Our relationship with our Spawn is... something like a queen ant and her workers, only each one of them has their own sapience and they are not bound to our will, and will not die if we are not there. They are capable of living on their own, even if they are instinctively drawn to us.
They are able to speak, communicate, have emotions and thoughts and opinions, and many of us feel our spawn are our children. Especially myself, as they are all I truly have left after my original reality was destroyed. I am the progenitor of my race, a name which does not translate to your tongue, and I will not be bringing them back.
There are other Old Ones, but each one has their own workings. No two of us are the same. One thing that holds common among all Old Ones is that we are all capable of creating Spawn.
We have no need to reproduce at this point. Our reality is gone. Earth belongs to the Humans, not to us. So even if I had the opportunity to breed with another like me, I would not. My Spawn are good enough. They are like children to me, and they can not rise to take over the world even if they wanted to, for they can not breed. To truly make a dent, they must be able to breed so I am in direct control of their population.