In Macbeth, Act 3, Scene 4, Macbeth hallucinates when he sees Banquo's ghost. His fear and guilt begin to get the best of him. Lennox is present at this banquet. And in Act 3, Scene 6, Lennox suggests that Macbeth has killed Duncan and Banquo. The others disagree, but Act 3 is when some (at least Lennox) begin to suspect Macbeth.
In Act 4, Scene 3, Macduff learns that his family has been killed from Ross. Ross implies Macbeth's involvement when he says, "For that I saw the tyrant's power afoot" (IV.iii.186). Ross tells them that Macbeth is getting his army ready, then tells Macduff that his castle was attacked after this. Since Macbeth was getting an army ready then shortly afterward, Macduff's castle was attacked and his family was killed, Macduff (and Ross) surmise that Macbeth sent his army there to kill Macduff's family.
Having convinced Malcolm that he is the rightful heir of Scotland, Macduff is even more determined to seek revenge on Macbeth. Remember that Malcolm flees to England in Act 2, fearing for his own life after his father, Duncan, had been murdered.
By the time of Act 5, Lennox, Malcolm and Macduff are armed for battle with Macbeth. Malcolm is there to reclaim his rightful place as king. Macduff is there to avenge the death of his family. And Lennox had always suspected Macbeth's wrongdoing.
The thing is, most of the indications of Macbeth's crimes occur when he is alone or with Lady Macbeth. The few clues that the other characters see are with Macbeth's erratic behavior and suggestions from people like Lennox and Ross. They essentially have to piece it together themselves.