Open the alerts panel, then assign the squad to Active/Training (or establish a more complex schedule of alerts). This is accomplished by opening the m ilitary screen. Instead, you need to schedule his or her squad to train. You cannot directly assign a soldier to train. Aside from a few specific circumstances, wooden training weapons are not necessary for training, and can actually be counterproductive. Your soldiers will eventually pick up the equipment assigned in the military screen, though it is not uncommon to find them wandering around weaponless and half-armored when first drafted.
When soldiers spar or perform weapon drills, they practice (and thereby gain experience) with whatever weapon (plus armor and shield in the case of sparring) they currently have equipped. The weapons you wish your soldiers to use can be chosen through the military screen, and then the equip selection. Training takes many forms, from solo practice to direct instruction to sparring to actual (controlled) combats. Training is how you improve the combat skills of your soldiers in fortress mode.
