Stated baldly, a group of idealists, infiltrated and manipulated by ideological and economic rivals of Caesar, killed him in the Theater of Pompey where the Senate was meeting. Brutus, perhaps the most idealistic of the dupes, had a speech prepared for the occasion, but the Senate fled in terror. Caesar's body was carried to the forum where, after an emotional speech by Marc Anton, it was seized by the mob and cremated on a hastily build pyre, the site of which is still venerated more than 2000 years later.
As is often the case, neither the idealists nor the manipulators had any real follow-on plan of action. All of them were as dead as Caesar within a year, and Marc Anthony and Octavian (later known as Augustus) fought a bloody eleven-year civil war to see who would inherit Caesar's mantle.
The following Internet sites have the gory details:
http://www.geocities.com/tayo_akinde/Caesar/assasin.html gives a short account.
http://classics.mit.edu/Plutarch/antony.html Marc Antony by Plutarch
http://classics.mit.edu/Plutarch/m_brutus.html Marcus Brutus by Plutarch
http://classics.mit.edu/Plutarch/caesar.html Caesar by Plutarch
http://www.bibliomania.com/Shakespeare/Tragedy/JuliusCaesar/scene3.1.html Shakespeare, Act 3 Scene 1
PS: Caesar's temple, built by Augustus, was smack in the center of the forum on the spot where Caesar was cremated by the mob. The remnants are still there and can be recognized by a semi-circular shed roof. Walk behind a seven foot high wall of old tufa blocks and you will find a low mound on which Caesar fans (supposedly neo-Fascists) still place flowers.