Noname I will take some of these tips and add them to the OP, but I will add some of my own for now.
If you're losing REALLY badly, then there might be a few things that don't make sense on a basic level, so I will try to address them:
Put out as many units as you can reasonably afford! You want all of your units to level more or less evenly, and more units means that you have more chances to turn back the enemy if one unit is knocked out!
if you don't know how to deploy units, then you press Y while on the level map, select "deploy unint", and select the name of the leader of the unit you want to deploy. You'll be able to confirm which unit it is before you deploy it.
You can build and take apart units in the "Edit Units" screen on either the world map or the level maps, but in levels you can only do it with units you haven't deployed yet.
Characters need to be at a certain level before they can become different classes: Amazons become Clerics at level 4, making them the earliest and easiest class for low-level Amazons to become.
Early on in the game, it's worth it to use characters like Dragons or Gryphons on the front line because they have really high defense.
Equip items that you find! They are potentially very powerful, and will make your life a lot easier. You can see what a given item does by pressing Select on the Use Item or Equip Item screen.s