Step1
First, do some research. The internet contains many excellent vintage camera resources, including eBay (for pricing info), photoethnography.com, mattdentonphoto.com, and many others - just search for "Vintage Cameras." You will want to focus on sturdily built SLR and Rangefinder cameras from any era before the early 1990s - after this, sturdily built, metal cameras became virtually extinct. Major brands like Nikon, Canon, Minolta, Yashica, and Konica are excellent choices as many online buyers still exist, and you can almost be assured of a quality product. Also, find out what cameras currently have a 'cult' following - I.E. the Yashica Rangefinders, Olympus XA, and Canon GIII QL17. These cameras can fetch a much higher price than similar models.
Step2
Now comes the process of actually finding vintage cameras. The best places to look are thrift stores, garage sales, and estate sales. These resources may not have a great selection of cameras (as compared to a photgrapher's shop) but the cameras will also (usually) be selling for much less than they are worth. Drop by the same thrift stores often, as their stock changes daily, and watch out for "half-off" days as well. Some thrift store chains send all their cameras to a single location, so find out which stores those are.
Step3
Once you find a camera, evaluate it's condition. Try firing the shutter, turning the rewind knob, opening the camera's back, etc. Not all mechanisms may work without a battery, so don't be too concerned yet if the shutter doesn't fire. Check the battery compartment for corrosion - it can often be cleaned off, but bad corrosion may mean internal parts are damaged. Look through the viewfinder - you want a clear, bright view. If there is just surface dirt clouding the viewfinder, this can be cleaned - internal filth is a more annoying problem.
Check the lens for any signs of damage. A common problem with older camera lenses is mold, which usually looks like cloudy, spider-webby speckles on the front, rear, or inside surfaces of the lens. Small amounts aren't of great concern, but a large outbreak is nearly unstoppable and can eat away at the lens glass. Light scratches are not a concern, but deep scratching or heavy cleaning marks are not desirable. Also check that the focusing motion is smooth - often the lube on older lenses will deteriorate.
"Fast" lenses are often the most desirable, meaning those with maximum f-stops as close to f1.0 as possible, depending on the focal length. For example, a 50mm Canon FD lens with F1.4 may fetch $65, while a similar 50 mm lens with F2.8 may be worth much less.
Overall, of course, cameras in fantastic condition are the best finds; however, even badly damaged and non-functional cameras will sell if they are of a highly desirable model.
Step4
Most vintage cameras found in a thrift store can be had for less than 50 dollars. Make sure you are comfortable with the purchase price in relation to the condition and brand of the camera. Beware of stores that have very high-priced cameras. Though the prices may sometimes be justified, shops often randomly pick a sky-high price, then lower it until the camera sells. If your'e not sure about a certain camera's price, go home, research eBay for similar models, then return if the price is fair. The camera may be gone, but at least you didn't get ripped off.
Step5
Once you purchase a camera, take it home and clean it as best you can. There are many sites on the web detailing exactly how to clean/repair each specific camera. Search for your model and simply follow the steps. A clean camera is much easier to sell, and much more enjoyable to use.
In general, cleaning all dirt/debris from the camera body with a Q-tip soaked in water or vinegar is a good start. Also, many older cameras will need their light seals replaced - a fun project for handy types. The Matt Denton Photography site contains a great light-seal replacement tutorial.
Step6
Buy a battery and test all the camera's functions. Some older cameras use now-unavailable mercury batteries, so you may not be able to test these. Check online to see what type of battery your model requires - there may even be work-arounds for cameras that use unavailable batteries.
If you are able to get the camera working, take a roll's worth of pictures. Not only will you get to enjoy the new camera, but you'll be able to say it is fully functional when you go to sell it.
Step7
To sell your camera, eBay is the best choice. Set up your auction, sit back and wait for the bids to roll in.
Enthusiast 
