How can I quickly and successfully get rid of them? I have these tiny bugs and some white worms too.
I Have Gnats in My Houseplants
You have fungus gnats. They are a true pest. This article discusses them: https://www.gardeningknowhow.com/special/children/fungus-gnats.htm One thing I've learned over the years is that they ♥ wet soil. If you tend to keep your plants on the really moist side, lighten up some on watering. We have the most problem with fg's in the spring with seedlings, and it can be tricky, but by keeping the soil on the dry side of evenly moist usually works best for us.