Fungus gnats can be so annoying!
Household chemicals such as vinegar and peroxide won't kill the gnats, but can damage your plants.
Bt-i--Bacillus thuringiensis israelensis--is a least-toxic treatment. Yes, you can use Mosquito Bits or Mosquito Dunks, but there are several products that are easier to use. Gnatrol is a product formulated for use on houseplants. Just follow instructions to get rid of the larvae in the soil. Treat all of your plants at the same time.
This is unlikely to completely wipe them out forever, just re-treat when you notice even a few flying around again.
Yellow sticky traps will help catch the flying adults. They only live a week or two, so once you kill off the larva the adults will disappear shortly. Or let the sticky traps thin them out.
Some cultural practices can also help discourage them. Don't leave water in saucers. Let your plants dry out a bit more before watering. A thick layer of sand on top of the soil can keep the adults from laying eggs in the soil. I haven't tried it, but I've heard that they're not strong flyers, and a small fan that directs airflow away from your plants will keep the adults from getting back to the pots to lay eggs.
Bt-i is the least-toxic way to get rid of them. If you decide to nuke them, get a product with imidacloprid, made for houseplants. Bonide Systemic Insect Control Granules for Houseplants is one, there are others. Do not use it outdoors--it's very toxic to honeybees, butterflies, other pollinators and friendly insects in the environment. Use carefully only according to directions, this stuff is very toxic and bad for the environment. Again, treat all your plants at the same time.
Whatever you do, the gnats always eventually come back. Just keep an eye out for them and repeat the treatment as soon as you notice even a few. I end up treating my plants with Bt-i two or three times a year, this keeps them in check.