This text is quite dense... please read through it.
Alright then. Since you are willing to learn, Ill teach you the basics. But first, let me ask you what your definition of cheap is, since many builds here range from 20$ up to 170$ depending on the quality and design of the laser.
There are three components to a laser-emitting device. Power source, driver (current regulation), and diode. Thats all there is to it. Purchase a red diode for around 10 dollars, and that will get you started. Then get a driver (another 10 dollars) and solder on leads to the appropriate pins. This will regulate the power flowing to the diode so the batteries won't blow it out. Finally, purchase a power source. For red diodes, you will need 3 Volts of power and roughly 200-400 milliamperes of current for it to operate. Laser power output is determined by how many amperes are flowing in the diode (which can be adjusted on the driver board... more on that later).
For an absolute beginner build, here are the parts list... You may want the following parts. Furthermore, you can put it in a flashlight or some other 'host' which houses all the materials in a nice package that operates literally like a flashlight.
LPC-826 Red Laser Diode 650nm
Groove 2 Laser Diode Driver or Rckstr Microdrive v3 (both are suitable)
and those are the main components you need.
You may also want to buy 4.2v lithium batteries that can fuel this laser. Typically, people use either an AA size battery called a 14500 or a special larger battery called an 18650. These are used in laptops.
Set the driver to ~300mA to get 250mW (if I recall correctly) of 650nm light. To set the current, you will need to construct a test load and measure how many milliamps are flowing in the circuit. More on this in the links I provide. Solder on connections to the driver board, input and output. You may want to have a switch, so place it between the power source and driver, not the diode and driver. And there you go. Basic laser emitting device.
The cheapest laser-producing apparatus (I wouldn't really call it a pointer) can be built for a low 20-30 dollars.
DIY: How to Build a Burning Red Laser - YouTube
Styropyro does a nice job on his work here, and most lasers, when gutted to their absolute basic components and build designs look like this. It gets a bit more complicated when you put it in a flashlight, as a new electrical pathway must be provided to complete the circuit for electricity to flow and thus power the laser.
This is the most basic guide I can come up with. Putting it in a flashlight and beyond are far too complicated to explain in a single post. The concept is very, very simple, but there are a lot of small details.
Here are some useful links
http://laserpointerforums.com/f51/i-want-build-laser-thread-52972.html
http://laserpointerforums.com/f51/dtrs-reviews-tutorials-modifications-compilation-53944.html
The first link will lead you towards a highly in depth overview.
The second will lead you to an aggregate of very high quality tutorials on how to put lasers in flashlights. These tutorials use high power 445nm diodes like I have told you about, but you can easily substitute them out with the setup I have provided you.
Lastly, remember to search around on the forums! More than 99.9% of all the questions you may have have already been answered. This forum has been around for years, and questions like these have been floating around waiting to be answered.
