Let's begin by looking at each character's final lines:
"No, no, the drink, the drink,--O my dear Hamlet,--
The drink, the drink! I am poison'd."
"Exchange forgiveness with me, noble Hamlet:
Mine and my father's death come not upon thee,
Nor thine on me."
"O, yet defend me, friends; I am but hurt."
I can definitely see how these lines are typical of each of these characters. Gertrude is shocked that she has been poisoned (completely clueless to the end that Claudius is exactly what Hamlet said he was), but in her last moments she shows her love for Hamlet by saying, "O my dear Hamlet".
Laertes shows his noble character by wanting to make things right between Hamlet and himself before he dies. He lets Hamlet know what has happened and says there is no longer any bitterness or contention between the two concerning the deaths of himself and his father, Polonius. It is interesting to note, however, that he makes no mention of Ophelia...hmmm...
And finally, Claudius' final lines show him to be exactly what he has been throughout the play - a coward and a liar. He asks his "friends" to defend him, though he is getting exactly what he deserved.
Check the links below for more information on these characters. Good luck!