Eight years ago when I purchased my road bike, I was talked into a triple chainring for the build up. It seemed like a good idea at the time for the type of riding I was doing, but I rarely (like one particular hill, once a year) use the (granny) ring and for various other reasons I'm wondering what I need to do to convert to a compact double chain ring. I'm guessing that it's not as simple as removing the small chain ring. The crankset is a Shimano 105 with Shimano Flightdeck shifters.
Tsapp

so your front derailleur is made to accommodate up to 3 gears but that doesn't mean it wont do 2. you will have to have the low limit screw adjusted, and your front derailleur shifter wont work properly. For everything to be kosh you will need a new front derailleur (specifically made for 2 chainrings), a new crankset with only 2 chainrings (your old one probably has the bottom 2 chainrings attached with the same bolts, if you remove one chainring then the bolt wont fit properly, a new 2x left shifter to replace the 3x shifter.

Amusing is incorrect, your front derailleur will work ok after adjusting for 2x. To use a 3x shifter on a 2x crank use the middle and outer shifter positions, if you shift into the inner position the cable is slack.

In any case, why bother? You'll spend money on a crankset and have less gear options with a small weight savings. I would leave everything as it is and enjoy the flexibility a triple gives.

Older (FC-5703 and earlier) 105 triple cranks use 130/74 mm bolt circles so the smallest middle ring that will fit is 38T and 39T is by far more common. You cannot convert it to a compact (50/34) double since the 34T chainring can't be mounted. To have a compact you will need a different crank.

I agree, either lock out the granny ring with the low limit screw or retain the versatility of a triple.

I would just buy new 5800 compact with a 11-32 combo the groupset is pretty cheap and will be great. the 34-32 will get you up anywhere I am guessing.