I'm trying to model one of my D&D characters in blender. I've already thrown together a rough reference sheet, and I've gotten decently far on her head. I'd like to at least rough out her horns before I move onto the body, but I realized that I made a grave mistake: I have no clue how to extrude part of her head in a way that would let me shape her horns how I want without wrecking the mesh. Is there anything I can do to work around this? I'd really like to keep it all as a single mesh, if possible. Please let me know if you need me to elaborate on anything, or provide something to help!
You need to make sure that you have enough geometry, i.e. 4 squares, then you make a 8 vertices circle (ShiftAltS to transform to sphere) that you can extrude.
There are no doubt many ways to go about it, but what I'd do is just knife (K) the shape of the horn, delete the faces in the middle and extrude the ring up as desirable.
I wouldn't. I would model the horns as a seperate object, and then, using a multiresolution modifier, I would sculpt some detail on the head, around the horns to make them fit. Then I would bake the sculpt as a texture and use it as a bump map for the character. (comment if you need more detail)
I would model the Horns as a seperate mesh either in the same object or a new one, or you could add topology to her head using "stars": The one on the left is a abviously a star, the one on the right not so much so I've numbered the same faces on both. It's about how the faces connect not about the shape, this "star" formation lets you split geometry while maintaining quads which will keep your mesh more neat.
You can see here that I've double the mesh resolution where the horn is by spitting using stars.
Just keep in mind that this will make it harder to UV unwrap (they mess with loop selection) but it's a lot better than having triangles.
I think those are your only options if you want to keep the resoulution of the rest of the mesh as is, the only other way I see is to just up add more loopcuts and increase the resolution of the whole mesh.