What we know:
As far as we're able to tell, Metal Gear Solid: Ground Zeroes takes place after the events of Metal Gear Solid: Peace Walker in 1974, mostly likely immediately after. The military base shown in the trailer, Camp Omega, is an American "black site" located on the southern tip of Cuba -- "A slice of American pie on Communist soil, and out of U.S. legal jurisdiction."
The small boy being held in the cage is Chico, a child soldier of the Sandinista National Liberation Front and eventual member of Big Boss' private military company Militaires Sans Frontières, who supplied intelligence during the events of Peace Walker. After the initial dialogue between Chico and The Disfigured Man -- our working name for the mysterious figure in the trailer -- the radio chatter we hear is a conversation between Naked Snake/Big Boss and another unknown member of Militaires Sans Frontières.
The woman mentioned during their conversation is Paz Ortega Andrade, also known as Paficica Ocean. Paz was a pivotal character during Peace Walker; a triple agent that infiltrated the Militaires Sans Frontières, the CIA and the KGB in order to further the agenda of Cipher, an organization that would later be know as The Patriots. As her body was never discovered after the aquatic destruction of Metal Gear ZEKE at the end of Peace Walker, her whereabouts have been unknown until this trailer, where we learn that she was discovered by fishermen and is currently being detained in Camp Omega, along with Chico.
Naked Snake/Big Boss' mission is to infiltrate Camp Omega, rescue Chico and Paz and deliver them safely to Mother Base, Militaires Sans Frontières' off-shore headquarters.
What we don't know:
The identity of The Disfigured Man is the most obvious and glaring omission from our understanding of this scenario. Initially we thought he may in fact be Major Zero, but Zero's physical appearance at the end of Metal Gear Solid 4 refutes this. Whoever he is, he appears to be a commanding figure in, if not the leader of, a new military group called "XOF," which apparently has unknown affiliations with the United States government and is obviously FOX backwards.
We also don't know how Chico was apprehended or for what reason, or how much time has passed between the events of Peace Walker and Ground Zeroes. Given the fact that Chico has not obviously aged and Paz would have had to have only been in the ocean for a survivable amount of time, however, chances are that it hasn't been long. Mother Base's continued existence and functional operation is another strong indicator that the game takes place in 1974.
That's all we got.
We're sure we'll know more as more assets and trailers for the game come out over the following months/years, but for now, we heavily encourage rampant speculation in the comments below.