How do I get rid of fungus gnats in my houseplants?

The adults you are swatting are the least important part of this. They live about a week. The population lives in the top layer of your potting mix, where larvae feed on fungus in permanently damp soil, and that is where this actually gets solved.

The likely cause

Fungus gnats need moist surface soil to breed. Nothing else in your home offers that, which is why the pots are the source. Kill only the adults and a fresh batch emerges days later from eggs already laid. Break the breeding cycle and the whole thing collapses on its own.

How to fix it

1. Dry the top of the mix. Let the top few centimetres go properly dry between waterings. Larvae cannot survive it. This one change does most of the work.
2. Water from below for a few weeks. Stand the pot in a tray, let it drink from the bottom, then lift it out. The roots stay happy and the surface stays hostile.
3. Put up yellow sticky traps. Lay them flat on the soil surface. They catch emerging adults before they can lay again and, just as usefully, they show you whether numbers are genuinely falling.

What to expect

Give it three to four weeks. Adult numbers should drop noticeably in the second week, as the existing generation dies off without replacement. Keep the traps up until you get a full week with a clean trap.