Baking multiple materials into a single UV for games?

I’ve been making a mesh from multiple individual meshes for the first time. They all have their own materials assigned to them. I’d like to be able to combine all these meshes together; the meshes would be joined, the UVs would all go to the same image, and I could export the whole thing for use in a game. How do I go about doing this? I think baking is involved, but I’m new to texturing.