Assuming that I have the capability to properly hold the instruments, what are the steps and instruments to use, to successfully (and optimally) perform a heart transplant without letting the patient's blood level get to 0ml?
This video will help you a lot.
The objective is 'simple': Remove the lungs and rib cages, cut the old heart using scalpel (or with the saw, if you like), throw it away, take the new heart and just place it inside the 'hole'. Done.
How to remove all those stuff is all depends on your skill and luck but I suggest hammer is the fastest way to break the rib cage without major blood lost.