In Shakespeare's Macbeth, Macbeth doesn't actually make any murder plan in Act 1--his wife makes the plan. She starts making plans the minute she hears of the predictions, and that Duncan is coming to her castle to visit.
The plan is to get the grooms who sleep just outside of Duncan's chamber drunk and drugged, and for Macbeth to sneak in and stab Duncan to death.
The plan works, and had Macbeth stuck to his wife's plan he might have gotten away with the assassination. But when he kills the grooms in the morning after the assassination, he casts doubt on his innocence and raises suspicion in at least one fellow thane's mind--Macduff's, who ends up being the one to defeat him and decapitate him.
Well, here's the whole brilliant (sarcasm) plot in Lady Macbeth and Macbeth's own words:
...When Duncan is asleep—
Whereto the rather shall his day's hard journey
Soundly invite him—his two chamberlains
Will I with wine and wassail so convince,
That memory, the warder of the brain,
Shall be a fume and the receipt of reason
A limbec only. When in swinish sleep
Their drenched natures lie as in a death,
What cannot you and I perform upon
The unguarded Duncan? What not put upon
His spongy officers, who shall bear the guilt
Of our great quell?
...Will it not be received,
When we have mark'd with blood those sleepy two
Of his own chamber, and used their very daggers,
That they have done't?
Who dares receive it other,
As we shall make our griefs and clamor roar
Upon his death?
So the plan goes as follows: When old and already tuckered out Duncan is asleep and his guards are almost dead from alcohol and drugs, Macbeth is to go in and kill the sleeping Duncan. Then he is to take the daggers from the knocked out guards, dip the daggrs in the King's blood, and smear the guards with the blood. Then he and Lady Macbeth are to quick put on their jammies and go to bed. Then when whoever finds the dead Duncan, Macbeth and his awakened Lady are to run downstairs and look all horrified and shocked. Does such a plan have a chance... are people that gullible?