Keep in mind, this is quick and dirty. Well, sorta.
Goal is to be able to fight all 64 GE Encounters and deep into GBG. This can take months.
There are two aspects to getting better at fighting. Building up attack capability and learning tactics.
1) Building up attack capability.
Build enough Barracks, your exact fighting technique will determine that. If you do a lot of wedge fighting (see below) you'll want 2 Heavy, 2 Art, 2 Fast, 2 Ranged, 1 Light.
Yeah, that's a lot of barracks and city space. Yer gonna fight a lot and lose lots of troops and score buckets of treasures from GE and GBG.
Increase your Attacking Troops combat bonuses. How high a bonus should you try to get? Enough to win all your fights!
Acquire and level Combat GBs (in rough order, Zeus, CdM, CoA, Traz, TA, Kraken, AO) and get attack boosting Special Buildings. The fist four should be enough to get you through LMA, but adding the other three will make fighting easier.
Note: Won't cover how to use Traz, ask the person you buy the Goods from.
GE gets tougher as you move up in Era, you will prolly be adding to your attack capability for some tome to come.
2) Learning tactics: fighting the actual fight.
Don't autobattle. There will come a time when you will, but let's learn to fight first?
Learn the strengths and weaknesses of each troop, terrain effects, range, movement, and order in which troops move. You also need to study the defensive AI how it moves and targets troops. You also need to learn how to evaluate the army you are attacking and which troops you should use.
Note: I ain't covering using Rogues today. That's a whole 'nuther topic. Same for Champs, Drummers, Flags.
Fights through LMA break into two categories. Those with 3 or less total Artillery and or Ranged Units, those with more.
Select the troops you'll use based on the composition of the enemy army. Makes sure to check the troops ion the second wave!
Don't Autobattle.
Don't fight with wounded Troops.
Win the Artillery duel first.
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Wedge fighting:
My basic fighting formation against 3 or less Art/Rabged is a wedge of 5 Heavy and 3 Art . Place the 5 Heavy in a > anchored on the left border of the map. Place the 3 Art (you can use Ranged if there is no enemy Art) inside the >.
Once arranged, don't move. Repeat, do not break the formation. Wait for the enemy to come to you. Use your Artillery to kill their Artillery and Ranged units first. Do NOT move your Art out of the >! Then start shooting the melee units (fast, light, heavy) as they approach. Let their melee units come right up to the formation and hit your Heavies. you'll klil them on your turn.
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Against 4 or more Art/Ranged you'll want to use some combo of Fast / Light / Ranged / Art and be aggressive, but do not spread your forces out. Sorry, no one tactic will work , you'll need to experiment.
The entire time you fight, keep an eye on what the AI does. With each fight note what worked and didn't.
It's all about learning and experimenting, so work at it. It will take time - "Patience is the primary virtue of FoE"
Good luck.