You chose to lead the 3 of Spades.This is the correct leadWell done. You are signalling to your partner that this is your longest suit, that the card you are playing is your fourth highest, and that you have an honour in the suit.
Now the dummy is put down, and Declarer needs to decide how to play the hand.
You have contracted to make 9 tricks by your bid of 3
No Trump which means 9 tricks.
You can see 5 absolute certain straight off winners: 3 Aces, and the Kings of Hearts and Spades. In order to make at least 2 clubs, you need to lose the Ace of Clubs, and you will probably win an extra diamond, but it is not certain that you will win 2 of them. And so your nine tricks are not all that obvious.
Sort out all the hands now.
On the first trick, the lead was the 3 of Spades. You
assume from this that East has good Spades, so it is just possible that
your 9 might win the trick, so it is worth playing it to see. However,
West puts on the 10, so if you want to win the trick you have to play the
Ace. You can choose to not win a trick, which is called DUCKING,
but I don't see any real advantage of doing that at the moment as you have
a second boss card in Spades.
In No Trump, you do not want to play out all your good
cards first. You want to try to establish your longest combination of cards
in order to make some long suit tricks if possible, and to get rid of the
oppositions' high cards so you have control of all the suits.
Your best combination of cards is Clubs, so you would play them now, hoping to drive out the Ace, and then make the rest of the tricks in that suit. You start low from your hand, and if the Ace does not come up from East, you will play your Jack. However, we will say that East does play the Ace, so you will play the 2 from Dummy.
East has won that trick and he will again play Spades, knowing that he will lose the trick, but also knowing that his Queen will then be the boss card. So this time he plays the 4 of Spades, dummy will put on the 6, West will put on the Jack, and North has to decide whether to win the trick or to Duck. I suggest that he should duck. The advantage of ducking is that he still has control for the moment. If East plays Spades again, as is very likely, he will have to put on the Ace next time, being the only Spade left in the hand, but at least East will only have 1 boss Spade left, rather than 2.
So Declarer has lost 2 tricks, and won 2 at this stage. Since the Clubs are now established, it is just as well to collect those winners now, and he will play the King and Queen first, and then the 5, which will be won in the Dummy with the Jack.
Since you are in the dummy, you are set up for trying a finesse of the Diamonds. You have the Jack in the Dummy and Ace, Queen in your hand. If the King is on your left, you will capture it. If not you will lose the trick, because your intention is that if the King does not get played, you will let the Jack try to win the trick.
The King is in West's hand, and following the suggestion that you play an honour, on an honour, he will play the King, which North can then win with the Ace. It would not have benefited West to play low on that trick, because then the Jack would have won the trick, and this way it has cost Declarer two honours, and West does have the 10 left in that suit which might well turn out to be a winner, if he is lucky.
Declarer has now won 6 tricks. And he now plays the rest
of his winners, the Queen of Diamonds and the Ace and King of Hearts,
but has to lose the last Heart trick to West.
However he has made his contract of 3 No Trump. He scores 100 points below the line and that cuts off East-West's part score.
Go now to Lesson 11, which
is on 2 bids in suits other than Clubs.