In Scene II of "Hamlet", Claudius takes two actions to show he is an able administrator. What are they?

Yes,  he does. They're to do with the Norweigans, who there have been political problems with since before Claudius was on the throne. Here's what Claudius says

Now follows, that you know, young Fortinbras,
Holding a weak supposal of our worth,
Or thinking by our late dear brother's death
Our state to be disjoint and out of frame,
Colleagued with this dream of his advantage,
He hath not fail'd to pester us with message,
Importing the surrender of those lands
Lost by his father, with all bonds of law,
To our most valiant brother. So much for him.
Now for ourself, and for this time of meeting.
Thus much the business is: we have here writ
To Norway, uncle of young Fortinbras—
Who, impotent and bed-rid, scarcely hears
Of this his nephew's purpose—to suppress
His further gait herein, in that the levies,
The lists, and full proportions, are all made
Out of his subject; and we here dispatch
You, good Cornelius, and you, Voltimand,
For bearers of this greeting to old Norway,
Giving to you no further personal power
To business with the King, more than the scope
Of these dilated articles allow.
Farewell, and let your haste commend your duty.

Young Fortinbras thinks Denmark is weak, after Old Hamlet's death. He's been pestering Denmark with messages, and so Claudius has written to his uncle, Old Norway, to tell him to tell his young nephew to back off. There's the first decision Claudius makes - and it is a strong statement.

Claudius then moves neatly from political to private. Laertes wants to return to France, as he only came to Denmark for the coronation. Polonius gives his consent, and then Claudius gives his:

Take thy fair hour, Laertes. Time be thine,
And thy best graces spend it at thy will!

Claudius may be a villain. But he knows how to smoothly administrate the Danish court.