When Harry needed help escaping Malfoy Manor, Aberforth Dumbledore sent Dobby to apparate them out of there:
... the mirror fragment fell sparkling to the floor, and he saw a gleam of brightest blue - Dumbledore’s eye was gazing at him out of the mirror. “Help us!” he yelled at it in mad desperation. “We’re in the cellar of Malfoy Manor, help us!” The eye blinked and was gone.
(Deathly Hallows, Chapter 23, "Malfoy Manor")
Dobby would never be able to tell them who had sent him to the cellar, but Harry knew what he had seen. A piercing blue eye had looked out of the mirror fragment, and then help had come. Help will always be given at Hogwarts to those who ask for it.
(Deathly Hallows, Chapter 24, "The Wandmaker")
He wore spectacles. Behind the dirty lenses, the eyes were a piercing, brilliant blue. “It’s your eye I’ve been seeing in the mirror.” There was a silence in the room. Harry and the barman looked at each other. “You sent Dobby.” The barman nodded and looked around for the elf. (Deathly Hallows, Chapter 28, "The Missing Mirror")
So, when Harry begged for help, how did he know to send specifically Dobby?
Why did he pick Dobby and not another house-elf?
I can't recall a single evidence that anyone outside the Trio and Albus knew about Harry's relationship with Dobby; or that he used to serve Malfoys and would thus have an advantage.
How did he know Dobby - and how to contact him - in the first place?
He wasn't exactly on friendly terms with Albus, or with Harry.
And calling Dobby via house-elf means can only be done by employer (at the time, presumably McGonagle) and Harry himself since Dobby gave Harry his allegiance.