Unless you have been treating regularly, I think its a pretty safe assumption that at least one mound in their yard. I have many (way too many) mounds. I find them when I'm weeding my garden, in my veggie beds, along the sidewalk, next to my newly planted fig tree, and in the smack middle of the yard. They are huge, ugly, and ominous. Not since my graduate days studying and digging up fire ant mounds have I had as many stings on my hands and feet!
So... what to do about them? There are many options for fire ant control, so I'm going to give you the most common situation and my suggestions for control:
Fire Ants in Veggie Gardens. You have limited options here and must be careful to read labels to make sure they are labeled for use around vegetables. Boiling water and oils will work, but depending on how close that mound is to the plants, you may kill the roots. I suggest Spinosad as either a drench or bait. Both are labeled for use in vegetable gardens.
Fire Ants without Visible Mounds. Baits are definitely the way to go here. If you can't see the mound, you can't drench it properly. Baits are taken back into the nest and fed to everyone, including the queen. Baits may take up to 2 weeks to work, so be patient.
Fire Ants in Yards. My suggestion for this is to treat individual mounds and follow up a couple of days later with a broadcast bait. You will eliminate or at least reduce the size of the mounds you treat individually and the bait will help keep the populations down and knock out the mounds that you didn't see.
I'm Having a Party.... Tomorrow! In this case, you want to use either a broadcast granule or individual mound treatments.... or both. If the populations are super dense (like we are seeing right now), treat the individual mounds with a liquid drench or dust labeled for fire ants. Then do a broadcast granule to provide a barrier to prevent new mounds from popping up and treat the unseen mounds you missed.
Long Term Fire Ant Management. If you can't stand the emergency treatments and want to get on a regimen, baits are again the way to go. If the populations are fairly low to begin with, you can treat every 6 months. Treatments in the fall may result in no ants in the spring, in which case you can eventually drop back to once every 12 months. If the mounds are pretty dense, you may need to treat once and then again in 6-8 weeks. Then get back on the every 6 month routine.
As with all pesticide use - read the label first, apply only what is recommended, wear protective clothing, and don't overuse. One reason I like baits is that food for the fire ants and they are attracted to it. You end up applying less pesticide into the environment and usually get better and more long term results. If in doubt of what to use, see if an bait is available