Using two weapons simultaneously is much more difficult than simply picking up another weapon and flailing away. The two weapons must be used to complement, not impede, each other. How to accomplish this is the sort of knowledge a person with Second Weapon skill will have.
The application of this skill is very similar to that of Blind Fighting. To use this skill, multiply your character's skill in Second Weapon by the applicable weapon skill (the skill in the weapon the character is trying to use in their off hand), and divide by 100. The resulting number is the character's effective skill level when using that particular weapon in their off hand. To use this skill in conjunction with Blind Fighting, simply apply first one skill and then the other (the order doesn't matter).
Brutus has a skill level of 50 in Second Weapon, and a skill level of 84 in Knife. He is right-handed, so if he uses a knife in his left hand, regardless of what weapon (if any) he has in his right hand, his effective skill level will be 42(=50*84/100).