Responding to a One–Level Overcall
To show the difference between a weak hand with support for partner's overcall, and a stronger one, where you might actually make game, bid the opponent's suit! (e.g. 1♦ (1♠) p 2♦). It's called a "Cue Raise" and shows 10+ high card points. It tells partner you have points and trumps (three+), rather than a weak hand with trumps only.
It's forcing for one round, showing interest in reaching game. If the overcaller makes a minimum rebid, the cue-bidder may pass with 9-11 pts, raise with 12-14 pts, and bid game with more. e.g. you hold ♠K82 ♥A42 ♦Q763 ♣Q73 and the bidding goes: 1♦ from your left hand opponent, 1♠ overcall from partner, pass to you.Bid 2♦ to show a fit, and 10+ points. Partner will have an accurate idea of your hand, and be in a good position to judge where to play.
Overcaller’s Rebid after a Cuebid
The cuebidder doesn’t promise another bid if the overcaller merely rebids the suit, but anything else is forcing. Sometimes the overcaller may have a good hand with interest in game. If another suit is bid, it could also be interpreted as a help suit game try. Jump to game with help e.g. 1♦ (1♠) p (2♦) p (2♥) p 4♠. The 2♥ bid showed a better than minimum overcall, and asked for help in hearts. 4♠ said I do have some help.
What's Help? An honour or two, or a shortage, would constitute "help", in the suit partner asked about.
Handling the Opponents’ Overcalls
The overcall needs to be seen from the responder’s point of view. Often it can be ignored and the natural bid made. Sometimes an opponent’s interference leaves no choice but to pass (if you hold only a minimum hand of approx 6 points) and hope to get a chance to compete later in the auction. Although an opponent’s overcall does take away some bidding room, it allows you to use the same style as overcaller. e.g. 1♥ (1♠) 2♠ would show a good hand with heart support, whereas 1♥ (1♠) 3♥ would show a weak hand with four trumps.