I'm pretty tolerant of most lawn weeds, but I hate dandelions. Before resorting to round-up, does the boiling water method or the vinegar and water method really work--killing the whole plant--or is it an old wives' tale?
It's more of a wives tale. The vinegar and water only cook the top exposed part. You'll have to keep going back again and again. Pulling them with a good dandelion puller and aerating regularly to relieve soil compaction is the best way in my opinion. If you must use a pesticide, use a liquid spray that has 2, 4-D and Mecoprop in it and only spray the dandelion or other weeds. "Killex" is a good example. You can spray it to kill the weeds, but it won't effect the established grass! Glyphosates a.k.a. Round-up (Boo Monsanto) will kill every-thing. The small droplets can be carried in the wind and damage other plants too. Also, if you spray a glyphosate onto your grass and it kills every-thing in that spot and leaves a dead area, more weeds are just going to take advantage of the bare spot. If you can aerate your lawns, pull the dandelions now and then again in the fall to a lesser extent, eventually you will deplete the energy in any piece of dandelion root. And you won't have to use pesticides.
David is spot on with his advice. In addition, make sure your lawn is well fed so it can out compete weeds (lots of nitrogen, top dress with compost/peatmoss). When you cut it, cut it long (mower set as high as possible) so it shades out any weed seedlings trying to get established. With my soil I don't mind the dandelions as their deep taproots pull nutrients to the surface. I have my lawn tractor mower set to mulch so it all goes back and feeds the top soil. I do try to mow and mulch before they go to seed, but that can happen quickly in the spring.
Dandelion-pulling is part of my exercise & meditation programme. Just don't let anyone wearing shoes with higher heels on your lawn.
I've noticed running your lawn mower on its highest cut setting helps shade out the weeds and makes the lawn look lush, I give it a good scalp cut the last time all mow my lawn in the fall.
And leave a few dandelions blooming for the bees! They are an important early pollen and source for bees, and pretty too.