Beware, this will be photo-heavy -- but it's for a good cause. ;)
1. First and foremost, remember: you're buying vintage.
Short of buying from someone that you are sure knows how these cameras operate and have properly tested them to function, keep in mind that these cameras are probably over fifty years old by now. The Polaroid Automatic Land Camera model 100, the very first one, was released in 1963 -- that's older than my mom! You are buying vintage, and you gotta be prepared to maybe shell out some money on a risk. Luckily these cameras won't cost you an arm and a leg!
2. If you can, buy from a reputable source.
Had I known about this shop before, I would've bought my first Land Camera from this seller on eBay: option.8. This seller runs InstantOptions.com and I have seen him all over Polaroid forums on flickr -- this guy knows his stuff! Not only does he know these cameras inside and out, he's also able to modify them: the cameras he sells on his eBay store are all modified to take AA batteries, instead of the old, expensive, hard-to-come-by 4.5v batteries these take by default. Definite bonus!
If you're buying from a thrift or antique store, here are some major points to check out before buying:
3. Check the bellows.
One of the coolest things about these cameras is that they definitely look as old as they are -- and that's partly due to the large, folding bellows! It's important to ensure that these bellows are not torn, stiff, or just otherwise shifty-looking, since if light comes through, there goes your shot. While light leaks can add to a photo (like with a Holga), sometimes it can completely destroy it. Open the camera (here's a quick video on how to correctly do so here) and take a look at them, especially in those corner creases.
You should also open up the back of the camera and check the bellows from the inside. Looking at the back of the camera, you'll see two compartments:
Open up the film compartment, which is also where you can see the bellows from the inside, using the hinge on the bottom of the camera like so:
And hold the camera up to a light (with the bellows extended!) to see if you can notice any light coming through:
4. Check the battery compartment.
More often than not, if you buy one of these old cameras from say, a garage sale or a thrift store, depending on the model you might find that the battery compartment has corroded. While I have gotten lucky twice and haven't had this problem on either of the cameras I've purchased, I did find this problem with a Polaroid Land Camera flash gun I purchased from a seller on Etsy:
If you pop open the battery compartment (see #3, compartments photo) and you see any discoloration, corrosion, or anything that just does not look quite clean, I'd put it back. This is how you want it to look:
5. While you're at it, check the film rollers!
Pop the film compartment back open, and check out film rollers that are on the door of that compartment. You'll see instructions on how to unhinge the film rollers to inspect and clean them on the door itself:
Usually, you want to make sure they're free of any stickiness (which can result from pulling photos with developing chemicals through). Luckily, 9 times out of 10 you can clean them yourself. See a video on how to clean them here.
6. Lastly, look it over and make sure nothing looks broken (viewfinder/eyepiece, lens, etc.)
Use your intuition. If you can't see through the viewfinder or if anything glass looks fractured, if anything just looks not-quite-right, don't risk it.
Make sure the knobs and dials turn correctly:
(not noted on this photo: the blue switch next to the film speed dial, that's for light settings -- that should switch back and forth as well)
7. The last test - the shutter - is for when you have a battery.
Unless you're going to carry around a 4.5v battery with you whenever you are out looking for one of these guys, you will have to test if the shutter works on your own. This is risky, yes, but everything may look good but it could just not shoot when you put the battery in and try it out. Bummer, yes, but it can happen.
To check the shutter with a battery:
Leave the film out! It's not necessary for this part. If the bellows look good and there are no cracks or fractures in the camera itself, the film should produce pictures once it's up and running. Don't risk ruining a whole pack of film before you know if everything functions.
Hook up the battery. See #3 for where the battery compartment is.
Close the compartment, and aim the camera towards a light source.
Cock the shutter by pushing down on the #3 lever, the white lever sticking out of the side of the camera. It will have the #3 on it.
Press the shutter button (red button on top). You will want to hear two clicks. If you don't hear two, there's a problem. Two clicks means everything is golden; one or none mean the shutter isn't firing correctly.
If you don't hear two clicks, unfortunately I'm not sure what can be done. I would look around online to check for solutions, but as I've never had this problem, I can't offer any solid advice... I've got my fingers crossed for you, however!
If you've got two clicks, and everything looks good, well, you have yourself a pretty nifty new instant camera!
Note: These are packfilm cameras. They do not take any Polaroid 600 (self-developing/integral) film, like the ones you usually think of when you think Polaroid. They take pull-apart film, and Fujifilm is the only company I know of who continues to produce it. You'll want Fujifilm FP-100c for color film, or the Fujifilm FP-3000b for black and white film.
I would recommend taking a look at InstantOptions.com and Camerapedia for more information on how to operate these cameras, the differences between models, and so on.
I hope this helps, and if you do start shooting instant film, I'd love to see what you come up with! Have fun, and keep film alive!