Every meld on the table can be extended by anyone at the table. That includes yours, and that includes your opponents'. Use their melds as a safe home for the cards you can't place in your own hand.
When a player lays down a meld like 5♣-6♣-7♣, the group stays on the table for the rest of the round. On most Rummy variants, any player can add matching cards to it. If you have the 4♣ or the 8♣, you can drop it onto that run.
Same idea for sets. If someone melds three eights, and you're stuck with a fourth eight, you can put it on top of their set instead of holding it.
The card leaves your hand. It stops being deadwood. It counts zero points against you at the end of the round. The opponent's meld gets one card longer, but that doesn't hurt them either. They already scored the meld.
On Play Rummy, extending is a single drag. You pull the card from your hand onto the table meld and it locks in.
Most Rummy losses come from a small pile of orphan cards you couldn't fit anywhere. A lonely eight. A single Queen with no partner. A four of hearts that never grew a run around it.
These cards sit in your hand and count against you when the round ends. Face cards cost you ten each. Middle cards cost you their rank. If you're carrying four orphan singletons averaging seven points each, that's twenty-eight points of pure loss if the round closes.
Every opponent meld on the table is a potential exit for one of those orphans. The trick is spotting the match and using it before the round ends.
The habit is simple. Every time you take your turn, look at every meld on the table, not just your own.
Ask two questions for each meld. Can I extend this run at either end? Can I add a matching-rank card to this set?
If your answer is yes, extend. Don't overthink it. A card that's on the table is a card that isn't hurting you.
You don't need to remember which player laid the meld. It doesn't matter. Every meld belongs to the table once it's down.
Beginners forget to extend for two reasons.
They think a meld belongs to the player who laid it. It doesn't. It belongs to the table. The rules explicitly allow any player to extend any meld. Play Rummy shows this by letting you drag onto any meld, not just your own.
They forget to look. Players focus on their hand and their next meld. The table becomes background. Fix, force yourself to look at the table before every discard. Two seconds. If a card can go on any table meld, that card leaves your hand.
Once you're an intermediate player, you'll often have a choice. Two of your cards could extend two different table melds. Which one do you dump?
Rule of thumb, dump the higher-point card first. A ten-point face card leaving your hand is worth more than a three-point card leaving. Even if you could keep the face card for a future meld, the risk of holding it usually outweighs the reward.
Second rule, dump the card that's less likely to complete a meld inside your own hand. If you have a 4♣ that extends an opponent's run but also pairs with your 4♦, hold the 4♣. You might grow it into your own set. Instead, dump a truly orphaned card.
Extending is a great option, but not the only option. Your own melds are still worth more than one card extensions of theirs.
There are two situations where you should not extend an opponent's meld.
When the card you'd extend with is the seed of your own future meld. If you'd need that same card to complete your K-K set or your Q-K run, keep it. A future in-hand meld beats a one-card extension.
When extending gives the opponent a bonus. In some Rummy variants (rare but real), extended melds trigger a bonus for the original melder. If your variant is one of those, extending is a gift you shouldn't give. In standard Play Rummy, this isn't a factor, but check the rule set you're using.
Outside these two cases, extend.
This tip cuts both ways. If you meld a run of 4♠-5♠-6♠, an opponent could extend it with a 3♠ or 7♠ they were carrying. That's fine most of the time. It doesn't hurt your score.
But if the opponent dumps a specific card onto your meld that they'd have otherwise been stuck with, they just saved themselves points that would have hit your score at end of round. It's a small edge lost.
Experts use extensions for more than just point saving. Extending an opponent's meld is a free action, and it can be timed for effect.
Say you're one turn from declaring. You extend an opponent's meld to shed your last orphan card before your meld. Now your declare is clean. No leftover deadwood if the round ends before you finish.
Or, you extend an opponent's meld right after they've melded a new group, before they can adjust their read. The opponent thinks you were on offence. Suddenly you're one card lighter with no cost.
Extension is the cheapest action in Rummy. Free point reduction, free tempo control. Experts never leave it on the table.
Ignoring opponent melds because "they aren't yours." They are yours, in the sense that you can use them. Ownership of a meld is a myth after it's on the table.
Holding a card that fits an opponent's set "just in case." If the card doesn't fit your own hand and the round is winding down, extend. The just-in-case case rarely materialises.
Extending too early with a card you needed. Once in a while, a player dumps a card onto an opponent's meld that they'd have needed for a set next turn. Slow down. Check that the card is truly orphaned in your hand before you drop it.
Not looking at the table at all. The single biggest cause of missed extensions. Fix, always scan every table meld before you discard.
Play your next three rounds with a rule. Before every discard, name (in your head) every table meld and check if any card in your hand could extend it. If yes, extend before you discard.
You'll probably find you missed one or two extensions in each round. That's ten to twenty points saved just by looking.
After a few rounds, the check becomes reflex. You won't have to consciously scan. You'll just notice.
Extending an opponent's meld is the cheapest way to shed a card in Rummy. It costs you nothing. It saves you every point that card was worth.
The players who lose regularly hold their singletons out of pride or forgetfulness. The players who win regularly dump those singletons onto whichever meld will take them.
Look at the whole table. Use what's there. That's the tip.