What is the best way to get rid of weeds permanently?

to remove weeds permanently you must dig them out and get all the roots

Eileen is correct that you need to get out the roots but that just removes the plant you have. We have over-seeded the lawn to literally choke out the weeds and with consistent effort the lawn is full with only sparse weeds where there previously were many thistles and dandelions. Good luck and remember there is no quick fix and a perfect lawn resembling golf turf is only possible through chemical eradication - Killex or Round-Up.

Then you still have the seeds than will make new weeds, and seeds that will blow on your lawn from other properties. It's a never ending battle.

I tend to agree with the "never-ending battle" comment. But getting your grass or other chosen lawn plant to grow very thick is the most promising option. Concentrate on the health of the plants you like. Maybe dig out the weeds and sprinkle a little grass or mini-clover seed into the holes.

You can reasonably keep things under control by digging as soon as you see them, and using vinegar when they manage to sprout.

Here's a tutorial that might help https://chascrazycreations.com/home-made-weed-killers/

Hello, Hello, you can pull or dig out as many weeds as possible. Hope this helps, mix 1 cup of salt. 1 tablespoon of dish soap. 1 gallon of vinegar, pour into a spray bottle and spray weeds. Be careful not to spray plants that you love.

Here's a post that might help - https://chascrazycreations.com/home-made-weed-killers/

I have never have gotten very good results with any version of vinegar, dish soap, salt combos. Boiling water kills to the root, Eventually new weeds will come.