I use a gallon of pickling vinegar (7% acetic acid)
1 dash of liquid soap as a spreader.
I gently heat the vinegar until it dissolves the salt, mix it up with the liquid soap and then use it right way.
I've also used regular 5% vinegar with the same or slightly less effective effects.
3% vinegar doesn't work as well.
In repeated trials, this burns darn near anything it touches. Some leaves (sumac and aegopodium) burn in spots and are distinctly unhappy but recover. It took me 6 sprays this past summer (7-10 days apart) to kill a section of aegopodium. It turned the ground so acidic, we had moss growing there in the spring.
It is an effective and very low-cost burn spray. It burns what it touches and that includes good stuff and bad stuff. As indicated, repeated sprayings every 7-10 days are needed for perennial plants.
The current recipe I'm using is 7% pickling vinegar and a dash of soap and 2 tablespoons of vegetable oil. I have eliminated salt from the mix due to environmental concerns. I'm slowly finding where I recommended salt and deleting those posts.
I have decided to eliminate the use of salt as it really didn't help in my trials plus the polluting effects of using salt in the garden.
Test One
This recipe calls for combining vinegar and salt at 1 gallon of vinegar to 2 cups of salt. I did this and sprayed it around on a variety of test plants.
The results were not particularly surprising given the nature of the combination. There was a significant amount of leaf spotting and burning where the material had laid on the leaves. None of the plants was killed outright and all have rebounded as expected if you'd burn off the tops but not kill the roots.
The damage was limited because the spray didn't go on evenly (see test 2 below).
Plants with thick leaves (Aegopodium) were not bothered very much at all - no wilting or check in growth and only a slight discoloration of the leaf surfaces. Dandelions seemed the most sensitive as they curled up and browned off - I note though that these were the most heavily sprayed.
As a general rule, the thinner the leaf, the more damage was sustained. Grass was burned off with full coverage.
Test Two
I decided that part of the problem was the lack of a surfactant - something to spread the spray and enable it to cling to the leaf without puddling up and running off. So I took a few tablespoons of dish detergent into the next test. Same 2 cups of salt to gallon of vinegar.
The results were different. The dandelions were totally burned to the ground (see picture) These will regrow. This isn't going to be a lawn treatment as you'll also kill the grass around the dandelion as well. Grass also browned off.

Dandelions in Bark Bathway
The mature thistles I sprayed started wilting within a half hour of
spraying, looked quite ill at 5 hours but at 18 hours had rebounded to
upright with burning and spotting on the leaves. Not a kill at all for
this highly touted organic weed killers

Thistles burned
Virginia Creeper and Sumac were not touched although the leaves are heavily spotted.
The
Aegopodium is severely burned but not wilting or looking like it has
any intention of laying down and dying. This was heavily sprayed.

Damage to Aegopodium from
organic weed spray
Crown Vetch has been burned including the flowers that were in full bloom.
Bottom Line
It
has a variable impact on leaf surfaces in my trials depending on the
plant. The thicker leaved and aggressive growers seem to be the least
bothered.
Updates
I have
experimented with this homemade organic weedkiller for several years
after I wrote this original report.
The addition of soap is critical while the salt is not critical.
It takes several burns to
kill off perennial plants and sometimes several years (can you say
Aegopodium?) to really whack the plant to the ground. Several years
later, I'm still pulling noxious spreaders out of my front gardens as
the seeds germinate.
Environmental Impact of Organic Weed Killers Using Vinegar and Salt
It
is well known that salt has a negative effect on the growth of plants
(the Romans pretty much took care of the Carthaginian Empire by salting
their fields after the third Punic war)
The problem for us is the
long term effect of salt. It is washed down into the ground water by
rains and in some areas and climates, this is going to be a problem.
Vinegar
(acetic acid) is being used by itself in stronger concentrations in
commercially available herbicides to burn off plants. These products
work quite nicely while household vinegar by itself has a limited effect
on plant leaves.
Can I recommend Vinegar and Soap as an Organic Weed Killer?
Yes, it does have the ability to burn off some plants and some people consider it a good organic weed control combination.
No - it is not useful on lawns where you're concerned about overspray and burning off grass as well.
Caution:
Do wear protective breathing masks when spraying these products -
whether you mix them yourself or purchase commercial equivalents. The
tiny spray droplets are quite acidic on lung tissue.