1) At the very beginning of Act I Scene 1, the two sentinels, Bernardo and Francisco, confront each other during night watch. Bernardo asks, "Who's there?" Francisco insists that it is the other man who must identify himself: "Nay, answer me. Stand and unfold [identify] yourself." This scene hints to us that there will be dangerous circumstances ahead.
2) Again, in Scene 1, we learn that some "dreaded sight" has appeared to some of the sentinels. No better way to build suspense than to suggest that ghosts are running about!
3) In Scene 2, we learn that the previous King has died and the new King's marriage to the Queen has been accompanied by a "dirge." Yet we are not given any information about how the King has died. Unexplained death is always a good suspense-builder.
4) Again in Scene 2, we learn that Denmark is being threatened by Fortinbras of Norway, who is demanding the return of lands that had been lost by his father. Possible War = Suspense.
5) In Scene 4, Horatio, Marcellus, and Hamlet wait for the appearance of the Ghost, at midnight on a "nipping" cold night.