Metering is the process by which an automatic camera figures out the light on the subject, and then calculates the proper exposure so the person has the perfect amount of light on them. This system is inherently flawed, as it can only measure the reflected light off the person, and not the original light.
In the simplest sense, a camera is trying to change its exposure so the majority of the light coming in as measured to be gray. It tries to minimize the amount of pure black and white. In fact, it wants the color to be what is known as 18% gray.
The camera measures light in much the same way that the camera sensor does, it has a few photosites to catch photons, and then it measures the amount of photons and assigns this a value. The value is an integer between I and X (1 and 10), and is know as a light stop. A light stop of V is 18% gray, or the value the camera wants everything to be.
The only difference is that there will only be a few photosites for metering, as compared to millions on the sensor, and the meter does not care about color. Once the camera knows the exact amount of photons and has assigned it a value, it can use a complex algorithm, which are kept secret by the camera companies, to calculate the exposure.
Autofocus is arguably the most complex system in a camera.
Autofocus works by diverting the light from the lens into a small autofocus sensor, near the base of the image sensor. This sensor detects where the light is originated, and tells the camera to focus forward, or backward.
There are many different kinds of sensors. The most common in modern video cameras is Contrast Detection. With this system, an autofocus sensor will look at the light intensity between two adjacent photons that have been caught in the sensor, and adjust focus until the intensity difference (also known as contrast) between the two is at a max. It will continuously adjust focus as the object moves, so this is the best for sports.
The other kind of focus is known as Phase Detection, and it is used mainly in modern picture cameras. It works by splitting a light beam in two, and then examining the wave properties of each individual photon on each side of the splitter. It electronically creates a graph of the waves and peaks of the wavelength, and compares the graphs of both photons. From this, it can find similarities and differences, and where there are differences it utilizes an algorithm to figure out whether the focus needs to be adjusted forwards or backwards, and by how much.