leofelixzhu:
Like when you tap on "Popcorn," how does it go to the specified power level and cooking time?
The fact that you're asking this leads me to believe that messing around modifying a microwave oven isn't something you should be doing.
A note of caution:
Microwave ovens (and their electronics) aren't toys; inside there is a high voltage (HV) transformer and a powerful RF device (called a magnetron) to generate the microwaves. Properly shielded inside the oven, these microwaves, at the output levels of a consumer microwave oven, are safe. When you start taking apart a microwave, though - all bets are off as to whether - when the oven is put back together - the shielding capability remains intact. While coming into brief contact with microwave energy from a consumer device won't kill or otherwise hurt you, prolonged contact can cause RF burns to the eyes and skin - and you might not know there is a problem until it is too late.
To answer your question, though - most consumer microwave ovens have only two power settings: HIGH and OFF. To have a different power level (like 50% power), the microwave oven's controller simply toggles the magnetron between those states as needed to output the proper amount of power. Let's say 50% power is equal to a 30 second cycle between on and off. So if you set the time on the oven to 1 minute, the oven would turn on for 15 seconds (HIGH), then off for 15 seconds, then on again for 15 seconds (HIGH), and finally off again for 15 seconds.
That's basically how all consumer microwave oven's work. I have read that there are microwave ovens that can do continuous PWM to control output power, but they must not be popular, or they are more expensive, or something - I haven't seen one personally. When you think about it, though, a standard microwave is doing a form of PWM - just with a long period between state changes.
The control of the power to the magnetron is handled by either a switched-mode HV power supply (on newer models usually), or by a large HV transformer (older). These convert the household mains AC into the high voltage needed to power the magnetron. The microwave's controller then turns on and off the mains AC power via a relay or a triac to ultimately turn the HV to the magnetron on and off.
leofelixzhu:
My main question is how to interface the microwave oven control panel. Any tips?
I wouldn't even bother. It would be better to try to reverse engineer and hack the existing on/off switching control of the magnetron (whether it uses a relay or triac control), or switch it on/off yourself with your own relay or SSR (or triac). Before doing so, figure out the basic timings of the power switching by running it with a cup of water inside - at the various power settings, and timing the on/off transitions. Make notes of all this, then write your software on the Arduino to provide the same timing control.