At the ceiling box - the ungrounded fixture conductors {aka hot} for the fan and lights connect to the black wire coming from switch 2. The white wire from the circuit power source cable is the grounded leg conductor {aka neutral} for both the fan and light. The black wire from the switch 1 connects to the black wire from the circuit power supply cable.
Wrap a piece of black electrical tape around both ends of the white wire going between the 2 switch boxes as well as the portion of white on this cable being looped thru the fixture box, as this wire is also being used as an ungrounded conductor {aka hot}.
Bare wires are together and grounded to box (if metallic) and if the fixture has a green wire or a grounding screw , it gets grounded also. Bares and green wires are equipment grounding conductors.
Be sure to read all documentation that comes with your fan / light combo fixture.
If you need onward power from the fixture then....
(1) If only switched power required onward then at existing fixture...
(2) If only unswitch power required onward then at existing fixture...
(3) If switched and unswitched power required onward then at existing fixture...
If you need onward power from the switch then....
This is not possible with this configuration as no grounded leg {aka neutral} exists at the switch locations.
If wiring multiple fixtures be sure to check the following guidelines concerning how to do it and what not to do: Wiring Multiple Fixtures.
If you are new at understanding the "politically correct" electrical terminology and need clarification of the terms used, we strongly urge you to read the Clarification of Definitions and Terminology guide. This will explain the terminology used in this article.