Changing Shimano 105 triple chainset to compact
To go from a triple to a compact, you generally need to switch the front derailleur for one for doubles (make sure it can be attached to your frame and the right cable pull; front derailleurs have different cage shapes between doubles and triples), the front shifter (if indexed; you need a double shifter rather than a triple shifter, and it needs to have compatible cable pull with the front derailleur) and if you're using a bottom bracket with a spindle (like a standard JIS/ISO bottom bracket, Octalink, etc.), you may need to have a different spindle length (to get the right chainline). And of course, you need the compact crankset (which is compatible with your bottom bracket).  

In your case, you have a hollowtech II bottom bracket (with a Shimano road group), so you need:


Compact Crankset which fits hollowtech II bottom brackets (reasonably common; Shimano, FSA, etc. make them)
Shimano road double FD (cheap; you can get tiagra or higher for only 20-50 USD)
Shimano road double shifters (Expensive; you only need front shifter for a double, but you may end up getting  a set in which case you need to match the rear number of speeds as well).


I'd suggest trying the triple for a while -- you may end up liking it despite it not being in vogue.