The appearance of the Super Saiyan 6 doesn't change much from a Super Saiyan 4, where instead of Red Fur, the whole upper area is covered with Golden Fur, and the hair is turned into golden like that of a Super Saiyan 3, and shaded red area under the eyes similar to Super Saiyan 4. The saiyan has White Electricity pulsing around them.
Whoever uses the Super Saiyan 6 transformation, he will be an extremely tough opponent, as the power levels of this form is obviously much higher than a full powered Super Saiyan God, considering that Super Saiyan God Goku wasn't able to beat the God of Destruction, Beerus, where the Super Saiyan 6 can beat Beerus with a single finger. Surpassing even a Super Saiyan 5, the Super Saiyan 6, is assured to be one of the toughest and strongest transformations in all Dragon Ball Z.
Super Saiyan 6 eventually changes the personality of whoever uses it, into a cocky-over confident character, even Goku will turn that way. But when serious, the character changes into a wild personality, stating that the Super Saiyan 6 cannot be defeated under any circumstances.
Super Saiyan 6's creation was after the Battle of the Gods movie, considering that Goku will make a comeback to Beerus with an extremely powerful transformation that can brush Beerus aside like an insect and forcing his attendant, Whis (who is much more powerful than Beerus) to a fight, eventually ending up in a tie. It was revealed then that Goku (who went Super Saiyan 6) was only using 50% of his Power, and he will use his full immediatly after the tie, thus beating Whis.
Vegeta, enraged that he felt he will never be able to surpass Goku, even after he admitted that he can't during the Buu Saga, he refused to be surpassed by such a huge gap, training in the Hyperbolic Time Chamber for over 3 Years, Vegeta asked Goku for a fight. Goku, going Super Saiyan God, was interrupted by Vegeta, and was asked to go Super Saiyan 6... Goku responded and went Super Saiyan 6 according to Vegeta's Wishes, then Vegeta, shockingly went to a form surpassing a Super Saiyan 6... Goku then, was happy that he will finally find someone he can enjoy fighting with. After being punished by the Powered-Up Vegeta, Goku as well went to the same form Vegeta did. Shocking Vegeta, then both going 100% Strength. The fight was thought to end in a tie, but Goku was able to make a gigantic Kamehameha, it didn't kill Vegeta, but forced him to give up.