The simplest answer is for you to do it yourself. Of course, if you're asking the question then that is most likely not a very probable solution. There are many things you can do to lower your cost, but more than likely you will never find cheap kitchen cabinets.
First thing is first, never go retail. The big, fancy stores are convenient and offer a smile, but never without a price. Do your research. If you're looking for cheap, then it's a good guess you're looking for factory cabinets, or box cabinets. In even some of the smallest towns there are wood suppliers, and cabinet shops that will order these cabinets for you, but there too, is another cost. Some of these cabinet manufacturers will allow you to order directly through them, but you don't get the large order discount. With this, you'll have to weigh the pros and cons.
Another thing is measurements. Do you possess the skills and know-how to measure your own kitchen for cabinets? If you don't, someone will do it for you, but it probably won't be free. Do you know that a walkway is required to be 36"? That an island must have outlets, or it cannot be fixed to the ground? Or that box cabinets come in 3" increments? All of that is useful, and seemingly arbitrary.
The following is a little how-to on, How To Get Cheap Kitchen Cabinets:
Before anything you want to decide on your range/stove, oven, refrigerator, microwave, sink, dishwasher, and the rest of your large appliances. Get specific measurements on each, because you are literally building your kitchen around these appliances. Most of these may look very much the same in size, but varying less than an inch can change a kitchen setup.
The second thing is trial and error with trying to figure a layout. Measuring your appliances, trying to squeeze cabinets in there, and still leaving yourself with enough room to get about the kitchen. Remember, the refrigerator, the stove, these don't usually sit exactly against the wall. Plus, you have to leave room for the doors to open.
There are two ways to work with a corner. A lazy susan, is a large corner cabinet, often with a spinning rack inside, but it is not a cheap kitchen cabinet. If you're serious about your budget then you'll probably sacrifice space for your wallet's sake. In that case, you'll have fillers taking up the corner. 6" on one side and 3" on the other butting up to the 6" piece. This allows a clean look and more importantly, so you can open your doors or drawers.
So you have your kitchen designed, but you just now remembered the counter tops. They have made strides in creating new laminates. You can have a finished wood edge, a rounded laminate edge, or even a beveled laminate edge. It is comparatively simple and cheap to install the fully laminated counter tops, but it doesn't quite have that extra zing. Getting the wooden edging actually brings us to our next topic, installation.
A professional cabinet installer will charge roughly 15-20% of the cabinets cost for installation. I've personally seen franchises charge up to 200%. Call around, get qualifications, and recommendations.
This has been a fairly lengthy process already, now consider, the plumber, the electrician, the new flooring, the painter(if you opt to not get pre-finished cabinets) have not even been brought up. Which just so happens to prove, there's no such thing as cheap kitchen cabinets, but it does get cheaper the more you do.