West (Dummy): ♠A65 ♥A87 ♦AQ6543 ♣5
North: ♠10842 ♥J103 ♦J102 ♣K72
West opened 1♦ in fourth seat. North passed again. East bid 1♠ and West elected to raise to 2♠ (rather than rebidding diamonds). East bid 2NT—which should have been alerted as the “Spiral” convention—East inquiring as to how many spades and how many HCPs West's raise includes. West failed to alert, and bid 3♦. East alerted 3♦. It was supposed to show 14 HCP and a 3-card raise in spades. (Ironically, West did have that!) East bid 3NT.
South (your partner) led the ♣3 and your ♣K wins the trick, as declarer plays the ♣2. Since you and your partner play fourth-best leads, you know that partner started with only four clubs [because the ♣3 is his lowest club] and Declarer started with five clubs.
There are two reasons to switch to the ♥J: (1) you don't want to help set up East's longest suit; (2) the ♥A is an entry to the long diamonds in Dummy. Your ♥J draws the ♥K from Declarer who then plays the ♣9 to your partner's ♣A as you follow with the ♣7 (current count). Partner returns the ♥4 and Declarer ducks to your ♥10. You play your last heart to Dummy's ♥A.
Double-Dummy Declarer can play a spade to his ♠K and make overtricks, but the normal human play is to finesse his ♠J. That loses to parner’s ♠Q who can cash the 13th heart for the setting trick.
North: ♠10 ♥109 ♦KQ10984 ♣AQ83
South: ♠A765 ♥J ♦A32 ♣K9642
East opens 1♥. South's best bid is double. You don't want to pass with 2½ quick tricks, and you don't want to lose the spade suit by overcalling that moth-eaten club suit.
West will raise to 2♥ and partner will jump to 4♦. This should show an excellent diamond suit (probably six of them) and a highly invitational hand. With your precious singleton heart and good controls, it is worth a raise to 5♦. Getting to 6♦ on your “magic fit” is unlikely to happen, but getting to game is reasonable.
If you decide to overcall 2♣, West will bid 2♥ and North will bid 3♥, showing a limit raise (LR+) or better for your clubs. You can temporize by bidding the spades. Partner, loving her singleton spade, will take you to 5♣.
My partner elected to bid 1♠ over 1♥ and West bid 2♥. I then bid 3♦ freely. We were vulnerable, so that should show an excellent hand and a good suit (probably six of them since partner has already overcalled a suit of his own). East rebid 3♥. South's bid should be 5♦. The logic is: partner has no more than two spades because she did not support your suit. That means the opponent's points are in hearts and spades. Your singleton heart is now golden, and partner has a singleton or doubleton spade.
Her vulnerable 3♦ free-bid without a fit should show a hand like one of these:
♠xx ♥xx ♦KQJxxx ♣AQx
♠x ♥xxx ♦KQ10xxx ♣AQx
♠Kx ♥xxx ♦KQ10xxx ♣Axx
♠Kx ♥xxx ♦KQ10xxx ♣Qx
Any of those hands will make 5♦ opposite your hand [assuming the likely heart lead].
Getting to good games and slams happens easily when you visualize your partner's hand and how it will fit with your hand. (Visualization also helps you recognize misfits and avoid getting too high.)