Help me to create a mesh similar to that of the drawing in bold below. Excuse me for my bad drawing skills.
You might want more universal method, depending on what's your goal exactly. Theres a modifier Shrinkwrap that projects one mesh to another. So you can project a mesh with complicated topology to another mesh (very useful for retopology for example).
Another way this can be done is using two bend modifiers and an empty.
First add a plane, and then add two loop cuts in each direction. In edit mode, rotate it by 90o on the X axis.
Next add an empty and rotate it by 90o on the Y axis
Finally, add two simple deform modifiers and set them to bend. on the second one, change to origin to your empty.
You should end up with this:
This method has an advantage over the other two - it can be adjusted.