It starts with a scale drawing on paper. My drawings are usually 1" = 1', and I divide them into a grid of 1" squares that corresponds with a grid of 12" squares on the wall. The grid technique dates back to Renaissance times, and it helps me enlarge the drawing accurately.
Above, I've done a lot of the underpainting in acrylic, which dries almost instantly. It's convenient, but it's not great for blending and the paint is transparent, so the brush strokes really show.
This is after about 7 hours' work. Today I'll be painting in oils over the acrylic. Oil paints are more opaque, dry much more slowly, and allow me to blend away brush strokes. Because I don't have to keep adding more layers to get what I want, it's actually much faster to use the slower-drying oils.
With oils I use an alkyd medium -- an additive that speeds up the drying time so that by the next day, you can run your hand over the surface. Very useful for murals, which are in danger if they're wet for too long.