Simply put, telecine is the transferring of film to to video.

Examples of DIY telecine:
Gorilla Snowmobilly
The Little Man
Prospector Pete No.1
Back Woods Slayer
Killer on the Trestle
The Fall

To compare, here is an example of a professionally transferred film:


DIY TELECINE (film chain)
a brief primer on DIY telecine:

First - when learning and practicing this process use some old stock. Do not use the film you are ultimately going to transfer. Each time you run film through the projector the film becomes a little more scratched and a little dustier. When you have your projector and camera set up to do the actual transfer run all the film at once in as few passes as is necessary. Consistency in transfer is what you want to try to get. There will be some dust and hair and scratches no matter what you do but try to keep that "look" consistent through out the process. If you use the actual print you are going to transfer when setting up the camera and projector what typically happens is that only the first 25-50 feet or so get run to set the camera and projector up. This means that the beginning of the film you are going to transfer is very dusty and the remainder of the reel or other reels are only slightly dusty. The result will be a noticeable difference between the transferred film after the cuts are edited. This can be very distracting to a viewer of the ultimately cut of the film. Consistent scratches are not as annoying.

The basic idea is to project the image to a screen and record the image with a video camera. The camera should be as close the projector as possible. And the camera lens should be the same height as the projector lens. Ideally the camera lens and the projector lens should be in the same physical location but this is impossible with out a high quality beam splitter so place them as close together as you can. Remember to always start the video camera before you start the projector and shut the video camera off after the projector.
Exposure is the most difficult part in making a good transfer. Just like you exposed the film to the actual image during production you now have to expose the video cameras ccd's to the projected image. Here is the rub - the film image has a wider dynamic range that the ccd is capable of capturing. This is the big reason film is better than video, but it also means that unusual techniques have to be used to properly capture the film image with video. I am going to describe this dynamic range of brightness just a little bit because it is the key to a proper exposure. Dynamic range in light is like the dynamic range in sound. In sound it means the difference between the loudest part of a signal and the quietest part of a sound signal. In light it is the same thing - the difference between the brightest part of and image and the darkest part of an image. Anther way to think of it is like this: Consider your video camera aimed at a white card. It's shutter, iris and the gain set at fixed values. The card is illuminated with a single variable intensity light. Turn the brightness of the light up until the camera reads the card as totally white. Just so the image is barely overexposed. There is a level of light that the camera will read as totally white, and any light brighter than that level will also be totally white (overexposed). If you were to dim the light from this initial value the camera would start to read subtle shades of gray, and the more you dimmed the light the darker the gray would become. Finally there is a low level of light, that the camera will read as totally black and and less light will also be totally black. Even though there still may be some sight hitting the card (visible with the naked eye) the card is still seen as black by the camera. These brightest and darkest points that the camera can read represent the width of the dynamic range that the camera can capture. Different cameras have different dynamic ranges. BTW I think that video-esse this is called the camera's "latitude." But all video cameras have a relatively similar latitude when compared to the wide latitude of film. So, your job is to reduce the latitude of the projected image of the film down to the latitude width that the camera you are using can capture. Here is what I do:
You have to get a fairly good gray scale printed on, at least, a 8.5 by 11 sheet of paper. You can google for gray scales used for video and print one of those. Place the gray scale on the screen area. Turn the , unloaded, projector lamp on. Frame the image with the video camera. Adjust the iris and or gain so that you get a proper exposure. If you have a well printed gray scale you should have values in the last few tones of dark greasy that all look black or the last few tone of light grays all look white. Set the camera so that the you can differentiate the all the values of the dark grays with the black still reading as totally black. With this setting you should have some of your light values on the gray scale reading as totally white. Here is the key. You need to determine the value of light gray that the video camera can still read with out being over exposed. This is an important value. This particular shad of gray is what color (specifically shade) that your projection screen needs to be for a properly exposed telecine. Using a gray screen will "compress" the projected light values. If you use to dark a shade of gray you capture image will look flat. It has to be the lightest shade of gray that will not result in the highlighted images of the projection being overexposed.

The next big hassle with telecine is matching the frame rates of the projector and the camera. With 8 mm or super 8 mm you can't really match the actual rate but you can match a harmonic of the one or the others frame rate. Without any film being loaded into the projector, or with some practice stock, run the projector. You will notice a flicker when the video is aimed at the projected image. First you need to set the video camera's shutter to the lowest setting possible usually this is around 1/60th of a second 1/30th is great but don't go below this. Don't worry unless you camera has some special feature it wont. now simply adjust the speed of the projector until the flicker is either removed or reduced as much as possible. This means slowing the projector down. The camera you are using captures 30 full frames a second. The super8mm projector is designed to run at 18 frames a second. There is a beat frequency of 1.67 between these two values, that is how many flickers per second you will see on the video camera. If you slow the projector frame rate down to 15 frames per second the flicker will disappear because you will be capturing two full video frames for every frame of the film. After the capture you will need to speed the capture video back up to normal speed. Increase the speed by 1.67 times. This should bring you close to the location sound speed. You may still have to tweak the speed to get it to match perfectly. For 16 mm or 35 mm the film frame rate is 24fps. Typically a special projector is used for telecine. Regular projectors use a 3 blade shutter, but telecine projectors use a 5 blade shutter. This create an effective frame rate of of 120 fps. So, you get about 4 exposures of frames of film for every full frame of NTSC video.