How do I turn on the self timer on a Power Shot A75?

Yes it does. See the "Using the Self-Timer" section beginning on page 62 of the manual: http://www.fixya.com/support/p900564-canon_powershot_a470_digital_camera/usermanual-A6A02C4-pdf

Press the self-timer button (marked with a one-handed clock) to cycle through the self-timer modes. Start the self-timer by pressing the shutter release button.

Full details are in the "Using the Self-timer" section of the manual (page 59 in my copy). If you need a manual, you can download one at
http://gdlp01.c-wss.com/gds/5/0900011235/01/PSS2ISCUG-EN.pdf

Press the FUNC/SET button. Use up/down to select Drive Mode (the rectangle, third item from the top). Use left/right to select the desired delay and press FUNC/SET.

The full instructions are in the "Self-timer" section in the manual (page 45 in my copy).

This sounds like it might be a defective CCD imager. If so, Canon should fix this for you for free, including free shipping both ways. This is regardless of your camera's warranty status. Please check this link for more info.

Applicable cameras include:
A40, A60, A70, A75, A80, A85, A95, A300, A310, S1 IS, S60, S200, S230, S330, S400, S410, S500, SD100, SD110, IXUS V2/300/400/430/500, IXY Digital 30/30a/200a/300a/D320/400/ 450/500

how do ifnd the self timer?

you can choose 2 or 10 seconds delay

1. Secure the camera to a tripod or place it on a stable surface.
2. Rotate the mode dial to [S], [P], [PICT], [AV], or [M]
3. Press the Power button turn on the Camera.
4. Press arrow [>] .
5. Use up arrow or down arrow to select the desired self-timer mode.
6. Compose your scene and press the shutter button.

• The self-timer function is activated.
• The photograph is then taken after the preset time.
• To cancel the self-timer at any time, press the shutter button.

After one shot is taken, the self-timer mode is turned off.
If you wish to take another image using the self-timer, repeat these steps.

Download user manual of Canon A75 camera by clicking Canon Support.
User manual has all instruction about this camera.

Instructions are provided on page 62 in the manual. If you don't have the manual, you can view / download it here.

Of course it does, it has full manual control (M), but may I suggest first trying "shutter priority" (Tv). This mode lets you set shutter speed up to 15 seconds, but it automatically sets the aperture to match the shutter speed that you set. Merely turn the mode dial to Tv, then use the right/left buttons to select the shutter speed.

Now before pressing the shutter button, may I also suggest that you use the camera's shutter delay timer to take the picture (this will eliminate any shake from you pressing the button). Just press the function button to bring up the menu. then find the timer setting (try 2 seconds).

Here's where you can download your camera's user manual if you want to read more on what your camera can do:

http://www.usa.canon.com/consumer/controller?act=ModelInfoAct&tabact=SupportDetailTabAct&fcategoryid=221&modelid=9828#DownloadDetailAct