Hi fellow gamers. I bought this game a while ago and find myself liking it more every day! One difficulty I am having is combat. I always seem to lose - even when the enemy would seem to be much weaker than I. Would anyone be willing to share their hints and tips on how to achieve success on the battlefield? Thanks!

Sure. Here's what I generally do:
On Attack:
If I'm trying to take someone else's town, i go with a mix of cavalry and artillery. It moves pretty quick, and you can get some fast attack combos happening if you do it right.
If I'm raiding another settlement, I use infantry and artillery. Four infantry and an artillery piece take quite a while to kill, even if they're getting charged by the cavalry. Raiding is all about turns spent in combat. The longer you spend in combat, the more you will steal (or eventually, destroy the whole damn thing).
On Defence:
Defence i'll usually have more cavalry/artillery, but still some infantry sitting around if I need them. If you're defending against a raid you'll want cavalry/artillery to move against the enemy quickest.
Bonuses:
Cavalry get an attack bonus from charging, ie moving into the square adjacent to them and then firing, all in one go.
If you mix different troop types (inf, cav, arty) in your attacks, you also get an attack bonus.
The ultimate bonus balance is the 3 unit types, a charge and a flank attack.
Also, there seems to be some hidden rule about the enemy retreating. It seems to be something to do with the strength of your units on the field as compared to your enemy's.

I'll add a few things..
First, balance your commanr unider. 12 attacks but 6 maximum units is useless. I usually try to get everyone to attack, especially when defending. Charisma means that your troops will not retreat under fire.
Another thing, later in the game, build a war academy (or something, don't remeber what it's called) and upgrade your units. The battle is dice-based, meaning that attackers and defenders roll 1d40 (1 dice of maximum value 40), the one with the maximum value wins. That's what I think at least. When you upgrade your units you'll get a +2 bonus to every roll. This means you'll troops will have better chances.
Then, when fighting, try not to kill your troops. If it looks like you are losing, retreat. This way your commander and troops will improve instead of dying, and you can use them more effectively later.
Happy hunting.

Yes, War Academy things are very useful. Although they do cost quite a bit of gold eventually. Lvl1 defense for each troop type (infantry, Cavalry, Artillery) will cost you a mere 500g each or 1500g total. You can research things as a once off sum or a per turn amount. It depends on your available resources as with all things.
As to the other Jhiltune said about commanders, he/she was very correct. 12 attacks but only 6 unit maximum is a poor choice. When purchasing leaders, the amount of points available to spend on their attributes is based on your Colony Centre's level and the level you have Leader researched at the War Academy.
If you can, aim for 7 attacks and 12 unit maximum as a good starting point. Under 5 attacks is bad, but 5 attacks is fine. 12 unit limit allows you to have a good mix of units, or 9 Cavalry and 3 Artillery (my personal preference for 'small' armies).

There is ONE exeption to this.
the general you have that defends a city do not need maximum units, focus on attacks on him. as he gets to use all units in that colony (until the max units in battle cap)

I have two things here that have not been covered...

#1 seems painfully obvious, but I'll say it because no one else has, upgrade your forts and build the (5) strength units fast as possible...

#2 Has to do with dealing with the computer players later in the game, I keep 2 "generals" with armies in my border cities at all times, Most often, the computer will seek to RAID your cities. Always come out with your strong leader and army and actually attack the enemy OUTSIDE your city. The raids can be devestating, and it's virtually impossible to kill off a 15+ unit army before they loot you 19% or more. (and though silly, even if you kill them to the man, they get that raided amount) I find that whats left after I rip them up outside can usually never raid anything before they are obliterated.

Hope this helps.

I think I will not agree with the above statement: In my opinion the general in the city will have the units attached to him plus the militia from the city(usually worthless) so the max units is still quite important. Am I wrong?

One tactic that works if you got a bit of a slog to get through is to cycle your cavalry so you get a charge bonus each round. To do this have a slot open in the back row or front row and 1 cavalry (or more) in each. Each round move back the cavalry in the front row and charge with the cavalry in the back row, more bonus if you have infantry and arty in support.

No, not from my experiences, It will use mostly your regular units. ofcourse, there will be militias too, so its possible that having large party capasity can prevent militias, having a large force, and attack enough to support multiple cannon/ infantery attacks really makes it worth it. ;)

I managed to have a Levl.4 Leader with these stats: 22 Units, 15 Attacks, 2 Movement and a Reputation of 6. Named him "Walter von Aue". He started of as a Level 4 with 11 Units 9 Attacks.
My start of Leaders are:11 Units 8 Attacks 1 Movement. 3 Artillery Units and 4 of Cavalry and Infantry. Good for shipping on a Levl. 4 Ship.

The War Academy is pretty good. My Leaders are on Level 6 upgrade. Units offensive on Level 4 and Defensive on Level 5.

And it does cost a lot of money!! Mind you, it still cost me about 3 Army's to capture an aprox. 15.000- 20.000 strong City.

The war academy is everything...also capture a war temple (usually leaving an exploror there will control it). I build level 4 leaders with 12 troop, 4 cav, 5 inf, and 3 art. You can transport by ship.

Also, i am not totally sure how it works (you may need to be a missionary & conqueror), if you find the ancient ruins and build colony nearby (you may need a war temple), build a level 4 church. If you tagged on the church, a box will pop up when you can summon a Crusader. The Crusader has more points to work with than creating a commander at the colony center. For what ever reason, the Crusader option does not alway happen.

I never buy charisma. I try to get to 13 attacks ASAP.....always adding troops along the way to ensure use of the attckes. If I get over 24 troops. I add movement. Don't forget economic warfare...post explorors by opponents resource multipliers to deny them the bonus!