how to form a curve onto a curved surface

You might need to be a bit more specific. I am not sure I understand your question.

Typically, if you have a specific section in mind that requires a transition, you would use a sweep through varying sections.

There are many ways to accomplish "surfacing" and "shapes" but your approach should be rather methodical for good control. If you just want to rough it out, you might look at the warp feature and move the marque to a more localized region.

If you are working with surface features, you can merge multiple profiles and follow through with a round feature.

These are only a few ways to accomplish basic profile changes.

You can draw a curve on a flat surface or plane and then project it on a curved surface by project command in model tab.

Here is my suggesion,

You may make a curve through the datum points or vertexes, and make it's both end points tangent with the appropriate surface, then just mark on a 'keep curve on surface' and select the surface.

You will notice the curve on the curved surface.