You may have seen perserved lemons in gourmet grocery stores, but they're fairly pricey considering it's really nothing more than lemon in brine. However, those are ready to use immediately, whereas if you make your own you do have to wait a minimum of 3 weeks before they're ready to use. But homemade preserved lemons are just as good, cost much less (if you have a lemon tree, it's practically free), and if you make a jar (or more) of them, you'll have enough preserved lemons to last a year (at which time you'll want to make a fresh batch, anyway).
Traditionally, preserved lemons are made with regular lemons. In the foodie world, Meyer lemons are popular because they're thinner skinned and sweeter. The peel (with pith) is considered the desired end product, but many people use the flesh as well, particularly in soups and stews where it'll just disappear. The longer they've been preserved the saltier they are, so watch how much salt you add to the dish when using preserved lemons -- always taste!
There's no real recipe to making these beauties. Sterilize a glass jar by running it through the dishwasher (with your other dishes, of course, no need to waste that much water on one jar!) or boiling it, completely immersed in water, for 10 minutes. Quarter your lemons, but don't cut all the way through -- keep them attached at the stem. I've also seen people make one cut almost all the way through, then turn the lemon 180° and rotate it to the side 90° and make another cut there, so that it's almost like an accordion effect. Both methods are pictured here, pick the one you prefer:
Have a big bowl of kosher salt ready (I used coarse salt, but it doesn't need to be), enough for all your lemons. Open your lemon and stuff salt in. Open the other cuts and stuff salt in there as well.
Put the lemon in the jar. Repeat, gently but firmly smashing down the lemons in the jar as you go, releasing their juices, until you've filled the jar about 2/3-3/4 of the way. Top it off with some more salt.
Ideally you'll have enough juice to submerge all the lemons, but you probably won't. Meyer lemons, which are what I used, are super juicy, but I still didn't have enough juice to reach the top. Many people recommend then filling the jar up the rest of the way with extra lemon juice from spare lemons, or even water, but it's not really necessary. Eventually, the lemons will release enough juice to submerge themselves (or if they don't, after the 3-week period feel free to add more lemon juice). Topping it off at the beginning aids in the fermentation process so that you're able to use them sooner, so if that's a factor feel free to do so.
Keep your lemons in the fridge. About once a day (or more), shake your jar of lemons (making sure the lids are tightly closed first!), redistributing the brine and getting the lemons at the top in on the action.
After about 3 weeks, they'll be ready to use. Cut off as much as you need for your dish, then return the jar to the fridge. The lemons should keep for at least a year.