Do you and your partner understand the meaning of sequences such as these:
1♠ - 2♠
3♦
1♥ - 2 ♥
2♠
1♠ - 2♠
2NT
These are game tries.
I've met many beginning bridge players who read books and sit in classes and fill in splinters and Bergen raises and Jacoby transfers on their convention cards and who, when I've sat down to partner them for the first time and ask them,"What sort of game tries do you use over 1♥ - 2♥ or 1♠ - 2♠?", stare at me as if I'm speaking Greek.
(Although I took a year of koine Greek in university, I've never been remotely fluent in it.)
A game try is just what its name implies: a bid that suggests that your partnership is on the brink of game, and solicits partner's cooperation in deciding whether or not to bid it.
You make a game try when you can see that you and your partner hold, say, 24 - 26 points between you; if your partner has a maximum for his bidding, you should be in game, but if he has a minimum, you should stop short.
A common situation is that partner opens 1NT (15 - 17) and you have a flat hand of 9 HCP: if partner has a maximum you should be in 3NT; if he has a minimum you shouldn't be. The natural way to convey this to partner is to respond with 2NT: he should pass with 15, bid 3NT with 17, and use his judgment with 16. This one's pretty simple, and most beginners have no problem with it (unless they use 2NT for some other purpose, such as a transfer; let's assume not).
A more complicated situation occurs when the bidding starts 1♥ - 2♥, or 1♠ - 2♠. Assuming that responder's raise shows, say, 6 - 9 points, opener should pass with about 16 or less (the total is 25 at most) and bid game (or force to game) with about 19 or more (the total is 25 at least); with 17 or 18, opener should make a game try, asking partner to bid game with 9, stop short of game with 6, and use his judgment with 7 or 8. The key to game tries is to help partner with his judgment.
The most common game tries (and, arguably, the easiest) are known as
Opener
♠ A K 8 7 2
♥ J 4 2
♦ 9
♣ A Q J 8
Responder
♠ Q 6 5
♥ 8 7 3
♦ A 7 5 3
♣ 10 4 2
1♠ - 2♠
3♥ - 3♠
With a minimum, responder stops short of game.
Opener
♠ A K 8 7 2
♥ J 4 2
♦ 9
♣ A Q J 8
Responder
♠ Q 6 5
♥ 8 7 3
♦ A 7 5 3
♣ K 10 4
1♠ - 2♠
3♥ - 4♠
With a maximum, responder bids game.
Opener
♠ A K 8 7 2
♥ J 4 2
♦ 9
♣ A Q J 8
Responder
♠ Q 6 5
♥ 8
♦ 10 7 6 5 3
♣ K 10 4 3
1♠ - 2♠
3♥ - 4♠
With a middling raise, responder looks at his heart holding; here his singleton fits well opposite opener's weakness, so he bids game.
Opener
♠ A K 8 7 2
♥ J 4 2
♦ 9
♣ A Q J 8
Responder
♠ Q 6 5
♥ 8 6 2
♦ K 10 7
♣ K 10 4 3
1♠ - 2♠
3♥ - 3♠
With a middling raise, responder looks at his heart holding; here his three small hearts fit poorly opposite opener's weakness, so he stops short of game.
If opener doesn't have a particularly weak suit, he can use 2NT or 3 of his major as a game try; these encourage partner to look at his overall strength and not concentrate on a particular suit. For example:
Opener
♠ A K 8 7 2
♥ K 4 2
♦ Q J 9
♣ A 8
Responder
♠ Q 6 5
♥ 8 6 2
♦ K 10 7
♣ K 10 4 3
1♠ - 2♠
2NT - 3NT
(Note that some players would open with 1NT, while others never open 1NT with a 5-card major.)
Opener
♠ A K 8 7 3 2
♥ K Q 2
♦ Q J 9
♣ 8
Responder
♠ Q 6 5
♥ 8 6 2
♦ K 10 7
♣ K 10 4 3
1♠ - 2♠
3♠ - 4♠
Here responder has a middling raise, but 75% of his high-card points are kings, so he calls it a maximum and bids game. If he'd had ♣ Q J 6 4, he would have passed 3♠.
(Note that some players use the bid of 3♠ here as a sort of preempt, not a game try; this is commonly called 1-2-3-Stop. Make sure you know how your partner uses it.)
There are more complicated game tries than these, but these should get you started, and should improve your bidding: now both partners get to use their judgment.