Anborn was a ranger of Ithilien under the command of Faramir, Son of Denethor. During the War of the Ring, he spotted Gollum in the forest of Ithilien, and at first, thought it was just a black squirrel from MIrkwood. He didn't slay him because Faramir would not have his rangers kill wild beasts without reason.
Later, Frodo was awakened by Faramir to go and see the Moon rise over Gondor. The descriptions of the moon rising, and the views from the Window of the Sunset, Henneth Annun were very detailed, telling of views of Ered Nimrais.
From the Window, Gollum was spotted fishing in the lake below. Anborn was the one to suggest firing at him, and had Faramir given the order to shoot, the destroying of the Ring probably would have never come to pass. Anborn then led Frodo down to the lake, under Faramir's orders, so that the hobbit might persuade Gollum into coming into the Henneth Annun. It was Anborn that tied Gollum up, and lifted him up to the Window.
To be a ranger of Faramir's took great skill. Anborn seemed confident in his ability to shoot the small, dark shape of Gollum at night, so most likely he was a great bowman. He was quite loyal to Faramir, and carried out all the orders given to him, even against his own judgment.
Anborn defended Ithilien when the Southrons attacked, and most likely was by Faramir's side when he recieved the black breath defending Osgiliath.