Control a microwave from my computer?
I assume that by "Microwave" you mean a domestic microwave oven. 

(1) The easy and obvious way is to access the existing controller via the keypad - either by using transmission gates across the keyboard matrix - which is easy and fast to achieve, or by simulating the key scan results that the onboard microcontroller sees.

It's quite likely that as few as 2 x CD4051 transmission gates would allow keyscan access - but this is not certain. Rows to 8 or less inputs of 1st CD4051m, columns to 8 or less inputs, join outputs. CD4051 datasheet here.

Similar to this but join output of both multiplexers.



You'd be dong this blind so could get lost.
 Monitoring keyboard beeper allows checking progress.
 If magnetron does not behave as desired you can reset it.  

(2)  Or - easy but more technical and higher risk - drive present microcontroller pcb outputs.

Be SURE not to bypass any safety interlocks.

DEATH OR SERIOUS INJURY CAN BE ACHIEVED WHEN DOING THIS



SAFETY INTERLOCKS:

Microwave ovens have more safety interlocks to prevent uncontrolled operation than do most other consumer devices.
 There is a reason for this.
 Things that chop, slice, grind, mangle and compress can be very nasty indeed and the reason for fitting the interlocks to stop them doing their stuff on you or your family, friends or random strangers is usually obvious enough.  

A Microwave oven can deal invisible death or blindness or other injuries without advance warning if it is permitted to operate when in an unsafe condition. I have looked at some interlocks used and was impressed at the steps they go to in a consumer product to foil the typical screwdriver poking, microswitch taping interlock overriding cowboy.  

My prior home oven had dual microswitch interlocks on the door catch that also required lock A to have fitted home before lock B could lock AND lock A worked in such a way that if you pushed in a straight bar / screwdriver etc it would fail to lock - you needed the tip of the hooked door catch to travel into position and then drop down before interlock A was closed and interlock B was potentially able to close.

If you value your sight or life or those of anyone who may approach within about 5 metres (guesstimate) of the device then DO NOT DISABLE OR BYPASS THE INTERLOCKS.
I say 5 metres as the about worst case, apart from just boiling your head [ :-( ], is probably to crack the door slightly to form a slot radiator and getting quite a tight 2.4 Ghz beam. I'd guess that by about 5 metres away inverse square law and unidealities would probably let you get away with feeling warmer than expected. But I'd not be volunteering in any tests to see if 5 metres was "safe enough" [tm].