You need to have a look at Claudius' prayer speech in Act 3, Scene 3. He speaks the following lines, wondering whether he can be forgiven for his crime:
I am still possess'd
Of those effects for which I did the murder—
My crown, mine own ambition, and my queen.
Claudius killed Hamlet for his crown (that is, to become King of Denmark), to serve his own ambitious nature, and in order to marry Gertrude, the Queen of Denmark.
In his admission speech (Act 3, Scene 3), Claudius bares all. He, in obvious turmoil, states how his "...stronger guilt defeats [his] strong intent..." (line 40) He is even brought to the point where he states his motives: the crown, his ambition, and the queen (line 55). Even though the murder he committed was awarded with power, pride, and a beautiful queen, the guilt his has acquired is much more prevelant and severe. At the end of his speech, he makes one last attempt for redemption; he cries to the angels, "Help, angels! Make assay./Bow, stubborn knees; and heart with strings of steel,/Be soft as sinews of the new-born babe./All may be well." (lines 69-72)
Quotes taken from The Norton Shakespeare: Based on the Oxford Edition.
polonius tells his son basickly tips through school.for example give thy thoughts no tongue nor any unproportioned thought his act. which means think befor you speak or actions speek louder then words.
where did Claudius send hamlet to get killed