In Act 1, Scene 5, the Ghost gives a full account of his murder and the false explanation that was given to the public:

'Tis given out that, sleeping in my orchard,
A serpent stung me. So the whole ear of Denmark
Is by a forged process of my death
Rankly abused.

The true facts, according to the Ghost, are:

Sleeping within my orchard,
My custom always of the afternoon,
Upon my secure hour thy uncle stole,
With juice of cursed hebenon in a vial,
And in the porches of my ears did pour
The leprous distilment, whose effect
Holds such an enmity with blood of man
That swift as quicksilver it courses through
The natural gates and alleys of the body,
And with a sudden vigor it doth posset
And curd, like eager droppings iinto milk,
The thin and wholesome blood. So did it mine,
And a most instant tetter barked about,
Most lazar-like, with vile and loathsome crust,
All my smooth body.

"Hebenon" is the juice of some poisonous plant.

"Tetter barked" means being covered with scablike pustules.

The Ghost's account of his death at the hands of Claudius is all that Hamlet or the audience receives. Hamlet believes it implicitly at the time, then has doubts which he resolves by staging the play-within-a-play, which causes Claudius to betray his guilt. At that point Hamlet tells his friend Horatio, "I'll take the ghost's word for a thousand pound" (3.2.274-5)