Diplomacy | Civilisation Stage Spore Guide

There is a thing called "diplomatic panel" - you can see it near the map. It show your relationship with other nations (ones with more than 2 cities). Giving them gifts you can make them like you more. Or make them more angry by your territorial expansion or attacking their allies. Each of your deeds changes the statistics, co watch out not to make them attack you.

It's hard have friends without giving them money and pay them compliments. But after some tame they would allow you to attack a city you choose..