The army has to start the turn in a province with the sufficinet training facility, for example, spearmen need spearmaker, and advanced units need the same facilities that are used to train them.
Select the army, then select the unit training menu, then drag the units you wish to retrain from the army onto the training queue. Units will be trained 1 / turn.
Note- when you retrain, you get all the armour/weapon/morale bonuses that units trained in that bonus would get when retraining, also, you keep the previous bonuses, such as valor, unless the unit is below maximum strength, in which case the unit will be reinforced with men that have the valour a new unit trained in that province would have, and the new valour is calculated same way as merging two units.
If you want to get really good quality troops as soon as possible, you can use 3 provinces together, build the necessary unit training facilities, after that, have province a build weapons smith (+ weapons quality), province b build armoury (+ armour quality) and the province c build churches etc (+ morale). Then train one unit in each, and make them circle each province, being retrained at each, this way, after circling the three provinces your units have better morale, weapons and armour. Possibly even better valour, depending on provincial bonuses and training facility level.
It's costs slightly more than having all upgrades at once, but it's much faster to have the provinces specialize, than to try make them all build all the buildings. You can do that later, of course, but at first it is useful to get as good troops as early as possible.
Hope that helps you.