It shouldn't really be called "training" your army as all you are really doing is "producing" troops. Yes, they get killed and yes you then have to produce more of them. They get more "trained" by you going through the research tree and unlocking "upgraded" troops as you go. Go look through the research tree and you will see what I mean. But, it takes a really long time. I found that it makes the most sense to keep trying to win battles with the armies you have instead of waiting for them to be more trained because by the time you get farther in the research tree, the enemies get tougher too.
And yes, it costs a lot of money to get more soldiers and a lot of time. It is a part of how you balance your resources in this game.