A parts car is a vehicle one buys not to run or restore, but rather to cannibalize for spare parts.
Why do this? Simply, if you require a lot of spare parts for a vehicle, it's cheaper to buy a junker that has the parts you need in reasonable condition than to buy those parts separately, new or used. Much, much cheaper; quite probably whole orders of magnitude cheaper.
As with any cheap method, there are drawbacks.
You have to do the work to find out which cars have compatible components to yours, and how to tell the difference. This, of course, depends on what kind of things you need. Major mechanical components, for example, are often shared between a number of different models; in addition, many manufacturers have several different brands but share car models between those brands. For example, the Ford Crown Victoria and Mercury Grand Marquis are the same car with different badges and trim, and most parts are common. On the other hand, the same model name in consecutive model years may be totally different cars.
Once you know what you have to buy, then what? You have to have a place to keep the parts car until you're done with it. This is often the hardest part. Some areas have local ordinances prohibiting non-running cars from being kept in a residential area, at least outside. Or your housing association or landlord may prohibit it. Check first! If you can't keep the junker outside but you have a covered garage, you may be able to keep the parts car inside and leave the good car outside, but that's quite a sacrifice (and may make it a lot harder to extract parts from the junker). Keep in mind that if it's just yourself working on stripping the parts car, it might take longer than you think - weeks, or even months - to get everything off.
You may also be able to rent space to store the vehicle, but keep in mind that vandalism is then a problem. Keeping it at a friend or relative's place is also an option, but there's nothing like leaving a junker car in someone's yard to strain a friendship.
Now you've got somewhere to put it, you also have to consider how you're going to get it there; a parts car will most likely be a non-runner. You can rent a car trailer from U-Haul or other such establishments, if you have a car or truck powerful enough to haul the parts car's weight plus the trailer's weight, and just importantly, a car solid enough to be able to stop such a mass. If not, and you can't con any of your friends into helping, you're going to have to pay someone to do it. This will cost you. You won't be wanting to buy a parts car from very far away if you have to pay for it to be trailered to your property, or you'll be paying more than the thing is worth.
The final thing you should consider before buying a parts car is that stripping it of all valuable parts is going to be a lot of hard physical work. Especially if you want big 'n heavy bits like the engine or transmission, or large pieces of sheetmetal. You'd better have a good set of tools before you consider this; even better, have a good set of friends to help.
In fact, buying a parts car jointly is a good idea if you can find likeminded individuals. Joining a car club for your model of car is a good way of finding them, as is joining and posting to mailing lists devoted to them. If you can find 3-5 people who all need parts from the same model of car, with minimal overlap of what parts are wanted, the cost goes down significantly, and the odds of at least one of you having room to store the car temporarily are good. Plus, with 3-5 people working on the car, you could have everything off it in a weekend.
With all that organised, time to search for a car! Look everywhere - local classifieds, Ebay, post to relevant mailing lists, and anything else you can think of. Make sure everyone knows you're looking for one.
Don't pay too much!
Once you've got the car, how you proceed depends on how long you've got to store it. If you have to get rid of it quickly, strip it of everything of value - even the stuff you don't want. With the advent of online auctions, you've got a great way to dispose of the stuff you don't want, for a profit, or you could put it in storage in case you ever need it.
If you've got the space for a while, you can take your time, but beware that a car with pieces missing will suffer accelerated corrosion, water damage, etc. if you leave it outside.
Either way, selling off parts you don't need may pay for the car, storage and towing, if you're lucky, and you get parts that are free except for your own labor. If you're really lucky, you may even swing a mild profit this way, but don't count on it.