What should I do if a city-state requests my support?

I'm in a game where Catherine's empire has grown to enormous proportions and started to attack city-states. When she attacked Dublin, which I was befriended with and which I depended on for food at the time, Dublin "requested my assistance." This was a good opportunity to declare war, which I was already preparing for. So I wiped out Catherine's units in and around Dublin. I have not received any thanks for it though, on the contrary, I was accused of trespassing in Dublin and the friendship ended rather soon.

I also remember supporting a city-state with unit gifts in a different game, which had zero effect as well.

What should I do to aid city-states in a war against other civilizations? Do I have to wipe out the entire opposing empire before my help is acknowledged?

I accomplished this once. Some things I remember:

• I had to weaken/kill off some particular number of units, 5 maybe?
• I think I had to do that fairly close to the city state.
• Once I did, they were my allies for a LONG time after. The relations boost was substantial.

You might have missed something else entirely. I know in the case of barbarian missions you must be the one to finally KILL the units, weakening them in any amount is simply ignored. Maybe that applies here?

On another note, gifting units provides only a minor boost in relations, nothing compared to fulfilling any request or any gift of gold. You should not bother unless you really don't want the unit you are gifting. (I let military city-states spawn units for me always, and simply give them right back if I don't need them.)

If you want the City State to live, and you're prepared for war, you could let them be captured, and then charge in and liberate them.

Not only will they then be your ally, but you also get their vote for the UN - in case your game happens to go down that route.

Of course this is a bit risky, you have to be ready to take out the enemies units, capture the city back from then and then you have to defend the City State from any counter attack (because it allies with you, it will then be at war if the enemy).

And this assumes the enemy will capture the City State, if they fail and make peace with the City State then you will have missed your opportunity to gain any influence...

Whenever a city-state requests my assistance against a civilization, what I need to do is to kill X combat units of that civilization. It doesn't have to be close to the city-state at all. Damaging enemy units does not have any effect at all - only destroying them.

I have done this many times, and I'm pretty sure that is the requirement. I don't know the reason for discrepancy between what you report and what I just described - maybe you just damaged the units, but Dublin is the one who landed the killing blow.

One important thing - make sure that the city state is actively asking for you to destroy enemy units. Click on them to see what they are asking. Even if they are in a war with some other civilization, they don't always have that "quest" active.

Barbarian units work differently; I think the requirement there is to destroy barbarian units (again, destroy; damaging them does nothing) within the city-state's borders.

Gifting units to a city-state is a horrible way to garner influence with them, as most units only give about 4 influence. (so 1-2 turns worth of postive malus)

Often when citystates are attacked, they'll offer a quest to destroy units within their territory -- you see this often with barbarians -- where whenever you destroy a unit within their cultural influence, you get a nice lump sum of reputation (though if you aren't at least friendly, you'll still be trespassing after you kill the enemy unit)

Something to consider: When you slaughtered Catherine's units, where were they located -- neutral / catherine's teritory, or that of the city state? In any case but the latter, you may as well have been at war with a fourth party; City-States are obnoxiously oblivious about this. If it didn't happen within their territory, they didn't see it. Period.*

*Applies only to "kill X units of civ Y" quests. They learn just fine when you disperse a barbarian encampment or conquer a rival city-state.