I'm assuming the basics of getting them to train have been done right, to wit:
- build a barracks and set it for the squad(s) in question to 't'rain
- make sure the military schedule for them has training assigned
- set the squad to 'active' from the 's'quad or 'm'ilitary screen
Recruits with no military skills at all will start out doing individual training to grasp the basics. If they're in a squad, they will then try to teach each other what they've learnt via demonstrations. If they've reached sufficient skill in something that allows active practice - e.g. combat skill with a melee weapon - they _may_ spar, gaining skill much more quickly and training their attributes. If you're starting with a squad full of raw recruits, you'll have to wait between a half and a full year before seeing your first sparring match. Currently, dwarfs love demonstrations _much_ too much, to the point that larger squads can completely block themselves from decent skill gains by starting and stopping demonstrations over and over, with minimal or no actual experience granted in the process. Keeping the squads small during the training process helps quite a bit, by making the skill gain only painfully, not insanity-inducingly slow (it can be as slow as one skill level per year in the 'main' skill like hammerdwarf, sometimes less).
As has been said, good 'drill instructors' (i.e. dwarfs who have both a decent 'teacher' skill _and_ decent ratings in skills worth teaching to the military) speed up the process a fair bit, but like with all skill advancements, getting a dwarf to high skills by regular training takes some time. I got recruits from nothing to elite in about two years by pairing a single recruit with a single legendary militarydwarf, but with better teachers and better planning, faster advancement in slightly larger training squads should still be possible.
Crossbows for the masses are still a good idea - this way, they'll at least go down fighting instead of running around like headless chickens when Goblin Claus comes down the chimney. Just put them all in inactive squads with little issued gear apart from the crossbow and a few archery targets to shoot at, most of them will be rated as 'skilled' or better, which helps their precision and reload times. Dedicated archery squads can be quite effective, but should be put in _active_ training. This gets them from nothing to elite in a bit over one year. All you need is a barracks, an archery target and lots and lots of bolts. Putting them into a hammerdwarf class after that would still be helpful, to improve their survivability by teaching them dodging and shield use.