Bah danger rooms, real dwarves use sparring. (yes I know it's a singleplayer game and folks can use what they want, I'm joking)
My own method is to just set them to train 2 months of each season to reduce the happy thought from long patrol and not allow my military to have any other labors. They will train normally for 2 months then train a third month on their own without being on duty because they have nothing better to do.
As for speeding it up Having a dwarf with high skill in both teacher and combat skills helps drastically, If I get one I usually make them my Commanders. The recruits having high skill in teaching also helps(sometimes the students will demonstrate what they learned to others) but high skill in student and observation is good for all of them. Of course that's only handy if you have one of those mods that have workshops to train student, teacher, and observation. Because your chances of actually getting a significant number of soldiers with even 1 of those skills is slim to none.
But the jist of it is that training is supposed to be slow. You aren't supposed to be able to train up legendary godslayers in a year like back in the 40D days. Training will speed up as they train longer, if it helps. Because as they train they will also gain student, teacher, and observer skills while learning their weapons, increasing their learning speed as well.