For us, ants would invade even if there was a tiny food crumb on the counter. I've learned that there can be no food crumbs anywhere, which is extremely difficult and requires cleaning and vacuuming all of the time. Also, making sure sinks and tubs aren't leaky because in the summer time they're searching for water.
We use chemicals / pesticides to deal with the ants, which isn't everyone's cup of tea. We set Terro Liquid ant traps outside (contains borax), where we notice that they're coming into the house. They eat the liquid and then take it back to their colony, spreading the poison eventually to the queen ant. There's also this stuff called ant chalk, which our landlord gets in China Town. You simply draw a line with the chalk and the ants won't cross the line.
Some natural ant killing methods are peppermint oil and water (mix together and spray it around), baking soda, cinnamon, D-Limonene, cucumber peels, and cayenne pepper.