Regal Farseer was a Prince, King-in-Waiting and then King of the Six Duchies, though he was later dubbed "The Pretender," as he knew that after King Shrewd died the real King, Verity, was still alive.
The third son of King Shrewd, his mother was Queen Desire. Regal was encouraged from an early age by his mother to believe that he was superior to his two older brothers (Chivalry and Verity) and had a better claim to the throne. It was rather thought his mother chose the name "Regal" to further drive home the point. As an adolescent, Regal was childish, immature and pompous. He was jealous of his older brothers getting big horses, when he was riding a pony; he resented their being together so much, excluding their baby brother. His mother had warned him, falsely, that his brothers might want to kill him.
When FitzChivalry came to Buckkeep, Regal, resenting his closeness to Verity and Shrewd, treated him rudely and condescendingly called him "Nameless the Dog-Boy." Regal frequently went out of his way to torment and bully Fitz. There was less than a decade's difference between their ages.
He was typically Farseer in physical appearance, with dark hair and eyes, and was considered handsome; he was rather prone to much primping, taking pains to take care of his looks and wearing elaborate dress. His brown hair was smoother than his brothers' and better tended, oiled, and often scented. He placed more emphasis on appearance than on behavior, in marked contrast to his brothers. He had small hands and feet, and was somewhat famous for them.
Coat of Arms
(There is an earlier description of his symbol as a Prince that needs to be added.)
He was irresponsible as a Farseer monarch, taking an unusually hard line with criminals, Forged ones and people with the Wit. He created the King's Circle, a gladiator-style ring where he pitted any willing warrior or criminal agaisnt a Forged one. He had not been properly taught to rule, being the third son. He saw King's power as something he wanted, like a child who wants toys, and as means to do whatever he wanted.
He became King through a series of convoluted and dangerous plots.
He plotted extensively against the perceived threat of his brothers; it is likely the "accident" that killed former King-in-Waiting Chivalry was instigated by Regal, and he plotted to poison Prince Rurisk of the Mountain Kingdom to make Kettricken sole heir so that eventually he could marry her, instead of Verity.
After Verity married Kettricken and eventually left to seek the aid of the Elderlings, Regal and his Skilled henchmen Justin and Serene killed King Shrewd. Regal imprisoned and killed Fitz (though Burrich figured out how to make this a temporary death); Kettricken fled into the mountains; Regal declared Verity dead and was crowned, though he knew his brother was still alive.
In the end
As Regal aged, his behavior went from borderline acceptable childish jealousy to unbecoming outright arrogance. He used his new position as King to do as he wanted, however ill-advised, regardless of the effect on the Six Duchies. Towards the end of his reign, Regal developed his mother's taste for drugs and had her same irrational behavior, showing especially when it came to his hatred of Fitz, whom he stopped at nothing to kill.
In the end, Fitz used the Skill on Regal to force him into loyalty towards the Farseer heir and Kettricken, though it was never found out how long this would have lasted, as Regal was killed in his bedroom some time later, most probably by a ferret.
The coterie which Regal's half-brother Galen, child of Queen Desire, had created was loyal only to Regal, not to the real Farseer king or to the line of Farseers in general. Regal wasn't formally taught to Skill as his mother thought him too weak and delicate for something she saw as labor and hard work. He had the Skill ability, as he was able to use it to talk to and punish his coterie using Will's power.
Regal had a fear of anyone different to himself, and would not stand to have someone who was "unwhole" in his presence. This fear was inherited from his mother and extended to include such people as the Fool (although the Fool served as one of Regal's servants for a time) and people possessing the Wit.