Is clean soil the requirement for Tayammum or can the hands be touched on any clean surface? What if no soil is available? Is one supposed to rub the dust on his face and hands?

Clean soil or dust is the requirement of Tayammum. Dust can be found on walls, tables and other surfaces.

It is not necessary to rub the dust on your face or hands. After rubbing your hands with dust you can blow it away and then do masah. This is because Tayammum is just a symbolic replacement of the real ways of attaining purity: wudū and ghusl. Ammār Ibn Yāsir while recounting one of his travels in which he did Tayammum says:

Then I rolled over in the soil [and offered my prayer]. When I mentioned this before the Prophet (sws) he said: It was sufficient if you had just done this: The Prophet (sws) touched the ground and then blew away the dust from his hands and then rubbed them on his face and arms up to the elbows.(Abū Dā`ūd; Kitābu'l Tahārah)