Shakespeare, as Ben Jonson remarked, knew "small Latin and less Greek." He worked, therefore, almost entirely from translation. Knowledge of Caesar was in general pretty well known in the Middle Ages, at least among the literate, who learned Latin at least in part by reading Caesar. Julius Caesar was written in or around 1599, and twenty years earlier in 1579 the first English translation of Plutarch, who was almost totally unknown in the west until the middle of the sixteenth century, was published by Thomas North. It is from this pretty much exclusively that Shakespeare wrote the Julius Caesar, although he diverged from Plutarch's account in some places, especially in order to compress action. North's translation, from which Shakespeare adapts several passages quite closely, was not, however, a translation from the Greek, but from an earlier 1559 translation into French by Jacques Amyot, the first translation of Plutarch prepared in a language other than Latin or Italian. North published two other volumes of the Vitae, in 1595 and 1603, but it was not until the 1683 Dryden Translation that English saw a translation based directly on the Greek.

XenophonTheAthenian is actually incorrect about Shakespeare working in translation. Jonson was a well-known egomaniac, and had a real chip on his shoulder about W.S.'s success given his lack of a university education. What Shakespeare had, and Ben scoffed at, was a grammar school education so steeped in Latin that an average schoolboy would have had a greater proficiency than a present-day Classics major.

Here are some places to begin: Geoffrey Bullough's Narrative and Dramatic Sources of Shakespeare details 14 possible sources (3 of which are translation of Plutarch's Lives...). I've read a lot of Bullough and trust his accuracy, although I haven't visited this volume in a while. He and Michael Spring agree with XenophonTheAthenian that W.S. didn't read Plutarch in Greek. That doesn't mean he worked mostly in translation, however--but that he consulted translations in this case (most likely because he didn't read Greek, despite his great proficiency with Latin). There is even a claim by Boecker at the beginning of the 20th century that the play owes something to an Italian poem called Il Cesare. I don't quite know what to make of this since there is no real reason for Shakespeare to have spoken or read Italian (unlike French, which was quite a la mode), nor evidence that he read Italian works which weren't in translation. Lawrence Mason has a pretty accurate, if dry, appendix of the source breakdown if you don't feel like reading in depth for a while.