As many people (should) know there are different types of units. I dont mean types as in swordsmen, spearmen, or even better, pikes, I mean types as in light, medium, or even better, heavy infantry.

First off:
Please be aware that some of this IS opinion, mostly where what infantry should do what, but none the less it should be mostly facts.
I will add more to this guide as my knowledge expands.

Here's the stuff:

Light infantry
Light infantry arn't really intended for long engagements, if anything, light infantry are ment for:

• Taking light infantry head on.
  
• Forest engagements.
  
• Flanking enemies, preferably stationary/in combat ones.
  
• Hit & Runs.

Light infantry should never take heavy infantry head on, that would be like swatting a mosquito before it bites you, if anything, light infantry should attack heavy infantry from behind when they're stuck fighting a unit in the front. Don't stay there for long! As soon as the enemy takes the impact get out quick!

Hit and runs are basically just that, hit the victim and then get out quickly once the damage is done.


A short anecdote:

While playing with barbarian axemen (light infantry) I managed to take out 5 units of hoplites (heavy infantry) that stupidly followed me into the forest, thought I was surrounded and I eventually lost, I still caused a load of damage on them.


Medium infantry
Medium infantry are the backbone to an army, they're the units that are out in the middle of the field on the front lines weakening the enemy. Things you should know about Medium infantry are:

• They're the units that are out in the middle of a clearing having a fight with the enemy. Not in the woods, not in the road, just out in the middle of that huge clearing/field/etc.
  
• Debuffed in the forests, Go in but be careful, you can be wiped out by light infantry in there.
  
• Italian swordsmen, as do some other roman troops, have pila (Lalt+right click, limited amount)
  
• Flanking is never a bad idea!

Heavy infantry
Heavy infantry are the back breakers! They take the damage and scoff at it saying "Ha! You think that hurts ME?" While ok in the fields and clearings, they do a much better job in the cites or on roads. Never go in the forest. Heavy infantry are for:

• Attacking enemies head on. (To slow to go around)
  
• Holding roads or the base. (Buff in roads)
  
• Taking missile damage for less capable allies. (Those shields should soak the damage right up, don't be stupid though, raise them for cover!)
  
• Intimidating the enemy. (I've never seen someone charge Hoplites without needing help.)

Never let any troops rout, if they do, they are a disgrace to their officer (you) and should take the death that is chasing them. Let each unit fight until the very last man. Believe in Bushido!

Not only the ground, but the overall enviroment affects how your unit performs.

Example
Horsemen which I forgot to include now that I think about it, can't charge as well in the woods because the trees are in the way.

Light infantry
Light infantry buffs show that they're more for fighting in the forests. Not only do they get a damage buff, but a speed buff, and more.

Medium infantry
Medium infantry don't really get any buffs to help them, they're more of the middle ground in this situation, nothing to majorly help and nothing to majorly hurt. They can go into the forests with little to worry about except a loss of speed, and they can go on the roads with nothing to really help except a gain of speed. Avoid swamps!

Heavy infantry
Heavy infantry have a major buff when fighting on roads, not only does speed increase, but almost everything else, accelaration, damage, a charge bonus too! This is where you wan't to be!

Horsemen
I don't use horsemen, so I wouldn't really know, but common sense says to avoid the forests, charge downhill, (duh,) and prefer roads.

A short anecdote:
While going for the tower in thermopylae, I brought with me 2 units of medium infantry, (italian swordsmen,) I captured the tower and saw that 2 units of hoplites and archers were approaching from the enemy's side of the forest. I quickly moved my infantry in line and sent 1 unit charging at the enemy. That one unit causes massive damage to the enemy and doesn't give until the last man. When that one unit of italian swordsmen gave way (killing one unit of hoplites and badly hurting the other) I sent in the other unit, all they had to do was wipe up what was left of the surviving unit of hoplites. Easy peezy. The lesson to learn here is that every type has their place. Medium infantry can survive quite well in forest encounters, but heavy infantry want to steer clear of anything involving trees.

Thank you for reading!
Check out my guide on pikes and friendly fire!
If you see me ingame don't be afraid to say "Hi!" It'll make my day.