Any good tips on getting rid of ants?

For the past couple of summers we've now had invasions of "flying ants". This year the flying versions have been accompanied by common black ants. Am i correct in assuming the flying ones are simply "queens" ?

It looks as though there must be a nest somewhere as they have come through the area near the door frame (french doors between house and conservatory).

The nuisance lasts about a week or so ...

We have them, also. They have been around for about 3 weeks and we discovered maybe a dozen on the carpet each day until we found the joint in the ceiling where they were coming in. Black Flag spray ended their expedition into the house.
You can tell if they are termites or ants by carefully inspecting their antennae and body parts. Termites have straight antennae, while ants have crooked or jointed antennae.
All ants have 3 segmented body parts, a head, thorax and abdomen. Termites have 2 body parts, a head and body. Hope this information helps.

I have never seen ants in numbers like these. I thought it was just our old house at first, with trails of hundreds slowly moving across my kitchen counters one morning! But since asking around, it seems they've invaded everybody's kitchens, at least here in the southern states. And in the kitchen, one has to be extra careful not to wipe out your family along with the ants, as far as poison goes...I've heard remedies from strewing dry grits on the counter [ makes them explode, alledgedly] to those silly ant hotels, which, I swear I have seen them walk up to, hesitate a minute - then take off in the opposite direction!

Any non -toxic [to humans] advice will be looked upon with gratitude.

Well, here's the Ants thread I started last year:
Ants!
Gee, almost exactly the same time of year, too. There's lots of good advice in these posts.

I found quite a good site about insects of lots of kinds, here's the ant page:
UCDavis ant page

Good luck!

If you can follow them back to the nest, you can pour a kettle full of boiling water down it. If the queen is killed, your problem is solved. The same goes for digging it up, finding the queen and killing her. This is not always easy or possible, but worth doing if the nest is accessible.

Can I add NOT to use boiling water on your lawn such as I did last year, it kills the grass!