Some skills you can automatically train when you are the right role, but others you'll have to buy at a guild before you can increase them at level up. 2nd weapon skill is one of the latter: you have to buy it from the warrior or bushi guild before it's in your skill list and you can use it.
Note that this means that when you gain guild level 4, you can get double strike, but you still need to level up before you can actually use it, because you need to get 2nd weapon as well. (I you're a high enough member of both guilds you can get both trait and skill immediately of course.)
And don't put your hopes too high yet: at skill level 1 you won't get many second attacks. But at level 5, 6 or something you almost always do. (Perhaps this is dependent on the opponent as well.)
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