The easiest way to get to Ushuaia is to fly from Buenos Aires. There are several daily flights and its a 3 hour flight.
Rates can fluctuate due availability.
A cool way (but long way) to get from the South of Chile to Ushuaia is by taking the combination of bus and ferry from Puerto Natales and Punta Arenas. The compnay that does it is Pullman Bus Sur but only in September to April.
It leaves every Tuesday and Friday at 07:00 AM from Puerto Natales and 09:00 AM from Punta Arenas and arrives at the Ushuaia bus station at 7:00 PM. It is $37 USD one way.