Is there graphic of typical temporal paths that stars take through the Hertzsprung-Russell diagram?
This is typically a bit tricky to show because (1) some phases (e.g. the main sequence) are much, much longer lived than other phases and (2) a number of phases are spaced very close together in HR-space.
Be that as it may: any elementary text book on stellar structure will guide you through the path of a star through the HR diagram, usually accompanied by pictures. The book by Prialnik on this subject matter, or Ostlie & Carroll, are both excellent.
There are a number of illustrations of this on the Stellar evolution page of wikipedia.
Roughly a star begins as a large but cool ball of contracting gas, to the right of the main sequence until fusion starts in its core.
Once fusion starts it has reached the main sequence. It gradually moves up as it slowly brightens during its life, and then moves to the right and up as it expands into a red giant. There are then some significant movements as heavier elements begin to fuse. Sun-like stars undergo a significant change when the helium fuses in a matter of days (or less according to some models), called the Helium flash. As this occurs, the star moves significantly down and left, back towards the main sequence, before expanding again into an even larger red giant. The expelling its outer layers in a planetary nebula, and rapidly moving to the left and down.
Larger stars undergo other fluctuations, changing from red supergiants, to Luminous Blue Variables, and Wolf-Rayet stars, and ending in a supernova.
There are several illustrations of this on the wikipedia page, but noting the sometimes significant differences between the diagrams suggests that this is a topic in which the details are not certain, in part due to the difficulty in getting observational evidence of changes in stars, which occur over very long time scales.