Mr Pistorius shot Ms Steenkamp, 29, a model and reality TV star, at his home in Pretoria on 14 February 2013.
State prosecutors allege the killing was premeditated, but he claims he mistook her for an intruder.
For the first time in South Africa, parts of the trial will be televised live. Media interest is high.
The arrest of the national sporting hero astounded South Africa.
The 27-year-old double amputee won gold at the London 2012 Paralympic Games and also competed at the Olympics.
State prosecutors say Mr Pistorius planned the killing and shot Ms Steenkamp after a row.
But Mr Pistorius says he shot his girlfriend through the bathroom door of his home in Pretoria after mistaking her for a burglar.
If found guilty of premeditated murder, he could face life imprisonment.
He has also been charged with illegally possessing ammunition.
Much of the case will depend on ballistic evidence from the scene of the shooting, correspondents say.
On the anniversary of the shooting, Mr Pistorius released a rare statement in which he said: "The loss of Reeva and the complete trauma of that day, I will carry with me for the rest of my life."
Last week, a judge ruled that an audio feed of the whole trial could be broadcast. Some parts will also be televised, including opening arguments, evidence of experts, police witnesses and closing arguments.
The testimony of the accused and his witnesses is exempt.
One South African TV station, MultiChoice, has set up a dedicated Oscar Pistorius Trial channel to provide 24-hour coverage. It is due to begin broadcasting on Sunday.
Defence lawyers had said it would prejudice proceedings.
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