Tools needed to perform groupset overhaul
A road groupset usually consists of a number of parts.

There are not many tools, and they are generally not that expensive.

With all the resources out there (youtube, sheldon brown website, etc) and basic mechanical aptitude it isn't a difficult task.

You need basic hand/bike tools, (hammer, metric allen keys/drivers, screwdrivers, pliers, socket set, torque wrench, etc)

In terms of specific tools for those components:


Bottom Bracket (BB)



  If Pressfit:
   A BB press, a BB punch/remover.
  
  If Threaded: A BB Wrench



Cassette : Chain Whip, Cassette lockring socket tool.  
Chain : Chain breaker, Chain tool or missing link pliers depending on chain
Brakes
Crankset : Pedal wrench or allen keys depending on the pedals. 


  Modern Shimano specific (like the 105 group): Hollowtech II crank arm installation tool
  Front derailleur
  Rear derailleur 
  STI levers (Shifters/Brakes)
  
  You will probably need to replace the cables, so a cable puller might come in handy. 


An optional extra that would come in handy and for future work on the bike would be a bike workshop stand I spent 100$ on mine and it has been excellent for regular maintenance and upgrading parts.