How is an exposure made when you take a picture with a digital camera?

Let's assume this is a film SLR with a dual curtain shutter since you didn't specify digital or not. When the shutter button is depressed, three things happen virtually at once. 1) the reflex mirror flips up to get out of the way of the light transmission. In so doing, it covers the focusing screen. 2) the lens "stops down" to the aperture chosen for the exposure by moving a series of metal blades (if it is to be less than fully open). 3) If the exposure time is equal to or longer than the flash synchronization speed, one curtain moves (usually horizontally), which uncovers the film opening for the set time. This curtain closes the flash circuit contacts and the flash fires while the film is completely uncovered if a flash is being used. Light transmits (not reflects) through the lens assembly to reach the film. The second shutter curtain closes, the mirror drops down and the aperture opens up again.

If the shutter speed used is faster than the flash synchronization speed, the second curtain begins closing before the first has finished traveling. This has the effect of passing a slit across the film. The faster the shutter speed, the smaller the slit, so this design is capable of producing effective shutter speeds of 1/4000th of a second or less. When the shutter is cocked, the film advances and the shutter curtains travel back to their ready position. Some cameras use a vertical traveling metal shutter made up of a series of blades. They typically do not have a following curtain, and the distance of travel is 33% less than a horizontal moving shutter. This means their fastest shutter speed usually exceeds 1/1000th of a second.

This is how the film is exposed to the light focused by the lens.

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