Dome switch keyboard
Dome switch keyboards are kind of a hybrid of membrane and mechanical keyboards. They bring two circuit board traces together under a plastic "dome" or bubble. The top of the bubble is coated in some conductive substance. When a key is pressed, it collapses the dome, which shorts out the two circuit traces and completes the connection to enter the character. The pattern on the PC board is often gold-plated.
This is a common switch technology used in mass market keyboards today. It's considered very quiet, but purists tend to find it "mushy" because the collapsing dome doesn't provide as much positive response as a hard closing switch. These are also a good choice for office or consumer environments because they share a certain degree of liquid resistance with their membrane ancestors.
Capacitive keyboard
In this type of keyboard, pressing the key changes the capacitance of a pattern printed on a PC board. Usually this permits a pulse or pulse train to be sensed. Unlike "dome switch" keyboards, the pattern will be covered by a thin, insulating film. Capactive keyboards are inexpensive, and resist wear, water, foreign objects and dirt. They are common in PC keyboards.
Mechanical switch keyboard
Mechanical switch keyboards use real switches, one under each key. Depending on the construction of the switch, these keyboards have varying responses and travels. The best tend to approximate the old IBM Selectric electric typewriter keyboard, which was considered the benchmark for good performance for many years. Because of the expense of placing a switch at each key position, these have fallen out of favour in recent years, despite their excellent response. Most IBM keyboards up into the PS/2 line were of this type, and considered to be among the best of breed, although some complained that they were "clackity."
Hall effect keyboard
Hall effect keyboards use magnets and "Hall Effect" sensors instead of an actual switch. When a key is depressed, it moves a magnet, which is detected by a solid-state Hall-Effect sensor. These keyboards are extremely reliable, able to accept millions of keystrokes before failing. They are used for ultra-high reliability applications, in locations like nuclear powerplants or aircraft cockpits. They are also sometimes used in industrial environments. These keyboards can be easily made totally waterproof. They also resist large amounts of dust and contaminants. Because a magnet and sensor is required for each key, as well as custom control electronics, they are very expensive.
Membrane keyboard
Membrane keyboards are usually flat. You would most probably see them on appliances like microwave ovens or photocopiers. A common design consists of three layers. The top layer (and the one the user touches) has the labels printed on its front and conductive stripes printed on the back. Under it is a spacer layer, which holds the front and back layer apart so that they don't normally make electrical contact. The back layer has conductive stripes printed perpendicularly to those of the front layer.
When placed together, the stripes form a grid. When the user pushes down at a particular position, his finger pushes the front layer down through the spacer layer to close a circuit at one of the intersections of the grid. This indicates to the computer or keyboard control processor that a particular button has been pressed.
Membrane keyboards don't generally have much of a "feel", so many machines which use them issue a beep or flash a light when the key is pressed. They are often used in harsh environments where water or leak proofing is desirable. Although used in the early days of the personal computer (on the ZX80, ZX81 and Atari 400), they have been supplanted by the more tactile dome and mechanical switch keyboards.
Other parts of PC keyboard
The modern PC keyboard is more than just the switch technology, however. It also includes a control processor and indicator lights to provide feedback to the user about what state the keyboard is in. Depending on the sophistication of the controller's programming, the keyboard may also offer other special features.
The processor is usually a single chip 8048 variant. The keyboard switch matrix is wired to its inputs and it processes the incoming keystrokes and sends the results down a serial cable (the keyboard cord) to a receiver in the main computer box. It also controls the illumination of the "caps lock", "num lock" and "scroll lock" lights.
To tell if the computer is crashed hard, press the "caps lock" key. The keyboard sends the key code to the BIOS code running in the main computer, If the main computer is operating, it commands the light to turn on. All the other indicator lights work in a similar way. The BIOS also tracks the shift, alt and control state of the keyboard.
When you press a keyboard key, you may think that you do so in a continuous and smooth motion, making firm contact, and then releasing the key. However the key actually "bounces" against its contacts several times before it settles into firm contact. When released, it bounces some more until it reverts to the uncontacted state. If the computer was watching for each pulse, it would see many keystrokes for what you thought was just one.
To resolve this problem, the processor in your keyboard (or computer) "debounces" your keystrokes, by aggregating them across time to produce one "confirmed" keystroke that (usually) corresponds to what you think is a solid contact. It could be argued that the dome switch technology outlined above owes its popularity to the ability of the processor to accurately debounce the keystrokes. Early membrane keyboards limited typing speed because they had to do significant debouncing. Anyone who ever tried word processing on a ZX81 will recall this.