As far as I know, you only need to able to have egg "pregnancy", egglaying, first (which you can get through vagina mutation), and then get an ovipositor organ through mutation (Which can be a penis or from clit granted you make your clit huge enough I think, I never done it through clit or tail, I just remember you can do it with tail as well).
Once you have the organs necessary the first thing you need to do is to be pregnant with eggs (the modifier for pregnancy, like 1st trimester, etc, changed to the egglaying one) and then before you had to go to "labor", you need to have sex with a person.
During sex, insert your ovipositor (clit or penis) to the target orifices (I don't think you can do it in a mouth, correct me if I am wrong) and then there should be an action to insert eggs. and there you go. you implant other with eggs, and you just need for them to hatch it (which AFAIK, is no different than how normal pregnancy for npc works)
If we're talking about how to get yourself pregnant with eggs, then all you need is just to change your genital to have capability of laying egg, have sex, and you got it. No need for the other partner to have ovipositor.
Why is this so complicated?