What advantages do you have when attacking a village in Civilization?
You get several advantages when attacking a village.

1. You are the attacker and know what units they have

Being the attacker means they must play the first unit.  Even if you have not bought any additional unit cards, have no combat bonuses, nor have any unit upgrades from technology, and attack with a single army, you can still win the battle off of this alone as follows:


The village plays a unit (without loss of generality, let's say an archer)
You play the trump to that unit (in this case a horesman), killing it without taking damage
The village plays the trump to your unit (a spearman), killing it without taking damage
Etc. (you play an archer)
Etc. (they play a horseman)
You kill their last unit (you play an infantry)


Result: you win, losing 2 units

The big piece of variance here is the innate strength of the units.  Units range in base strength from 1 to 3.  A good draw for the village means they may have units that are stronger than yours, whereas a bad draw could leave them with units weaker than yours.  If the average strength in your deck is less than 2, do not attack a village with only one army.  Another problem here is that, while you win the battle and get the village token, you may lose your army since you lost 2 units in the battle.

2. You can bring more than three units

By attacking with multiple armies and having bought extra units, you can attack with more that the three units.  Not only will this practically guarantee victory, it also gives you more options in terms of what to play, allowing you to send your worse units out first (causing them to die and improve the average strength in your unit deck) and have more options with trump units.  Here is an example battle with 5 units (assuming all units are base strength 2):


The village plays a unit (let's say an archer)
You play the unit that is trumped by that unit (in this case a spearman) on a new front, since they no longer have a unit that can trump it
The village already played the trump to your unit, so they must play the same type (a spearman), killing both
You play the unit that is the trump to their remaining unit, which you know because they always have the same unit composition (they have horseman left, so a you play another spearman)
They play their remaining unit (a horseman) on a new front, since anywhere else it would be trumped
You play your remaining units on new fronts since there is no benefit to killing the village's units


Result: you win, losing only one unit

While you could do this with only three units in your battle hand, it is much less likely, since it requires them to play a specific one of their units first, which they probably won't do (especially if they have been paying attention to your purchases).

3. You can have combat bonuses

A combat bonus is part of the determination of who wins the battle.  A battle consists of each side playing all of the units they are allowed to bring as a result of their battle hand size.  Units may be killed during the battle, and this death is permanent.  However, you need not kill units to win the battle.  The winner of the battle is the person with the highest total of strength of surviving units, plus their combat bonus.  So, while a combat bonus does nothing to keep your units alive, it helps in you being considered the winner of the battle, independent of what happened in the fighting.  Since villages always fight with 3 rank one units and have no combat bonus, the most strength a village can ever have at the end of a battle is 9, so a +10 combat bonus guarantees that you will beat a village regardless of what happens in the battle, even if you have no units in your deck to fight with!  Obviously this is an extreme example, but even in less extreme cases, combat bonuses help you get the village token regardless of in-battle losses.

4. Your units can be higher level

This is the big one.  The other boons help you win, and having more units can help a lot.  This one helps a ton.  The villages always have the same units and their units are always level 1.  That means they deal at most 3 damage and have at most 3 health.  If any of the units you have in your battle hand are level 2 or level 3, that means you can now be running around with guys of 4 or even 5 strength; 3 strength also becomes much more common among your units.  With several level 3 units, you can sometimes win the battle without losing any units at all.  Leveling your units makes the threat of the village getting a good draw just so much less scary.  If there are still villages left by the time you get level 4 units, go pick them up.

5. You can use other technology abilities

You can use abilities on technologies like Mathematics or Animal Husbandry to help you win the battle.  The villages do not have any resource abilities at their disposal.  Spending a resource to win the battle can be a bit silly though, since beating the village may just give you the resource you spent to capture it (using an iron to capture a village that gives you an iron is not a great use of time or units).  The exception to this of course is if you have some other reason to want to win the battle, such as getting a coin on Code of Laws.  Abilities like 'Animal Husbandry' though (which are free), can help you win a no-casualties battle, especially if you have higher level units.

Conclusion

No, you don't get free units or inherent combat bonuses when fighting villages, but you do get to bring all of your technological might against their primitive army.  Consequently, fighting a village right out of the gate is probably a bad idea since that is when you have the fewest advantages.  Wait until you either have two armies and five units to bring to the battle, or until you've gotten a technology to level one of your units so that you only have to lose one or no units fighting the village.  These are the same things you will want for fighting other players as well.  The things you want to have are:


Higher ranked units
Combat bonuses from barracks/academies
More units (note that this requires you to have both more units in your reserves and multiple armies to allow you to bring extra units into battle) 


One more thing to keep in mind: when fighting a village, killing their units doesn't matter; it's just about winning.  Consequently, don't waste your units that have a base strength of 3.  These units remain the best as you increase in technology; don't get them killed fighting barbarians.  Conversely, do lead with your units with a base strength of 1.  These units are not great to have in your deck and playing them early will not only cull them from your army, but will also force the barbarians to spend battle turns killing your crappy units instead of your good ones.