The method is pretty much the same every where I've seen it. Here's what I did.
1) I got some lemons. Now, I live in Michigan. At the moment, it's really cold in Michigan. Therefore, my lemons came from my local grocery store rather than my friendly neighborhood citrus grower, but if you find lemons at a good price this is an easy way to keep them.
2) I washed the lemons well. You want to make sure there is no dirt or residue on the rinds, especially if your lemons are not organic. Pesticide is not a tasty condiment.
3) If your lemons have "nubs" on the ends, like mine did, trim them off. Then cut the lemons into quarters, leaving them barely connected at one end.
4) I sprinkled the inside of each lemon with salt ( I used non-iodized, but kosher or sea would be better) and placed them in a non reactive container. I used a big mason jar. In between each layer of lemons, put in a teaspoon or so of salt and push the lemons down so they start giving off juice. When you put in the last lemon, add another layer of salt and mash them down so they are covered in juice. I ended up putting a little extra juice in, just to make sure they were covered.
5) Cover your container loosely so air can escape and leave them on your counter for about a week, making sure that they remain covered in juice. Then move to them fridge. All the resources I've seen indicate that they will stay good pretty much indefinitely.
When they're ready, use these lemons like you would use regular ones. Some people said they only use the rind, others used all of the lemon. I guess it's up to you. Just keep in mind that these will be salty, so I wouldn't suggest using them in desserts. They're meant to be a condiment and flavoring. There are other methods that include adding spices. If we like these, I may try some of those other recipes as well.
Let me know if you give these a try. I'd love to hear what you thought of them. I'll let you know how mine turned out in a week or two.