When partner overcalls, even though it's not mandatory to respond if you have nothing, it's a good idea to show support. With three + cards in partner's suit and 6-9 points, raise partner to two: ♠J105 ♥84 ♦J84 ♣AJ952. Your left hand opponent opens 1♥, partner overcalls 1♠, opener's partner bids 2♥. You would simply bid 2♠, showing a few points (6 - 9), and a fit for spades. 1♥ (1♠) 2♥ (2♠)
If you hold four cards and have a weak hand, 4-6 (’ish) points, jump raise to three (believe it or not): Same auction as above, and this time you hold ♠JT54 ♥8 ♦T854 ♣Q985. Although this hand is very weak, you show four-card trump support by jumping to 3♠. In modern bidding, jumps in competitive auctions are weak. Your jump to 3♠ is not asking partner to go to 4♠, unless they have six trumps. 1♥ (1♠) 2♥ (3♠)
If you hold five cards and have a weak hand weak, jump to game: You hold: ♠JT542 ♥8 ♦T85 ♣AT95 Your bid is preemptive, trying to take away the opponent's bidding space. They will probably make 4♥, but you bid 4♠ before the they reach their heart game. 1♥ (1♠) 2♥ (4♠)
What happens if you told a good hand for partner's overcall? Now you Cue Raise (bid the opponent's suit)
With four cards, a good hand (10+ points), and a fit for partner's overcall, cue bid opener’s suit: You hold ♠KT54 ♥82 ♦KQ5 ♣AJ95 1♥ (1♠) 2♥ (3♥) p 4♠ p.p.p
Bid the suit that the opponents opened. (Above = 3♥, showing a good spade raise with 10+ points). You're using the opponent's opening for your own purposes. It shows real values, and a hand interested in game.
If partner overcalls at the two-level, e.g. 1♥ (2♣), the same applies, but remember that now their overcall is stronger, showing a decent hand (12+) with a good suit. Jumps to game are preemptive, and a cue raise shows a good hand.
Change your bidding style when both sides are in the auction. It’s harder to tell who’s got what, and how far to go, so if partner overcalls, look at your trump fit rathe than points. The bigger the fit, the higher you should bid. Without a fit, it's better to pass and defend.