They were probably bred from the same hybridization process which bred the Uruk-hai. Only once are they mentioned in the books. In The Two Towers ("Helm's Deep" chapter, during the Battle of the Hornburg), Gamling, a man of Rohan, refers to the army bred by Saruman as half-orcs and goblin-men.
Frodo says to the Fellowship upon leaving Bree "So that's where that southerner is hiding... he looks more than half like a goblin'', referring to the Squint-eyed Southerner, an outlaw from Dunland and agent of Saruman selling Pipe-weed.
Half-orcs were the the product of the union of Men and Orcs, probably the same process which created the Uruk-hai. They were not as wide spread as Uruk-hai, but they were still deadly. It is recorded that Half-orcs came to be by an evil act of sorcery where Saruman bred Dunlendings with his Orcs. The evil Half-orcs were the result of this union.The Half-orcs were slant-eyed like orcs, yet as tall as men.They worked in the deep caverns of Isengard for years preparing for Saruman's conquest of Rohan, forging weapons and armor. It is unknown if they were Immortal, or at least longer lived than Men. They were part of the armies of Saruman who attacked Rohan twice in the Battles of the Fords of Isen, and of the 10,000 that attacked the Rohirrim in the Hornburg, where most of them perished at the Battle of the Hornburg, either before the fortress walls or in the Huorn's forest.
The rest of them were killed in the pits of Isengard, mostly because of the huge flood the Ents made when they descended upon Isengard with wrath. Some lived beyond that day of doom and followed Saruman into exile, even during the Scouring of the Shire, where they served the fallen wizard with others until his last breath. In the Shire, they were all killed along with their fellow villains the Ruffians in the Battle of Bywater and buried in the Battle Pit.
The first appearance of these half-goblins occurs in Fellowship of the Ring in describing one known as the Southerner, a spy of Saruman's;
In one of the windows he caught a glimpse of a sallow face with sly, slanting eyes; but it vanished at once. ‘So that’s where that southerner is hiding!’ he thought. ‘He looks more than half like a goblin.’
Further description follows in The Two Towers:
But there were some others that were horrible: man-high, but with goblin-faces, sallow, leering, squint-eyed. Do you know, they reminded me at once of that Southerner at Bree; only he was not so obviously orc-like as most of these were.’
In "The Scouring of the Shire", there is further mention of the half-orcs under Saruman's control, described as men having squinty eyes and sallow complexion (a description used to describe Saruman's spy near Bree at The Fellowship of the Ring, as well as some of the orcs in The Two Towers), which seems to suggest that they look mostly human but share some of the features of the orcs.
they were disturbed to see half a dozen large ill-favoured Men lounging against the inn-wall; they were squint-eyed and sallow-faced. ‘Like that friend of Bill Ferny’s at Bree,’ said Sam. ‘Like many that I saw at Isengard,’ muttered Merry.
‘Of all the ends to our journey that is the very last I should have thought of: to have to fight half-orcs and ruffians in the Shire itself - to rescue Lotho Pimple!’