There is no way to become a bridge expert overnight.
There is no substitute for years of reading, lessons and practice.
Not everyone can wait that long.
Accordingly, here are some "quick tips" for immediate improvement/results.
1) Review/study the basics. Know inside and out the first 3 bids of the auction (Opening, Response and then Opener's Rebid). You think you already know these? I doubt it. Almost all players have gaps in their fundamental knowledge. It will take a few hours, but the best way to review these bids is in this series.
2) Review/study the basics of defense such as: Opening Leads (Top of a sequence, 4th-best versus notrump), Second Hand Play (Second hand low), Third Hand Play (Third hand high, but cheapest of equals), Signals (Attitude is most important), Overall Defensive Strategy (Passive is usually best). Most matchpoints/IMPs are lost on poor defense. For help, see this book.
3) Study the basics of Declarer Play and understand the difference of planning at Notrump or a Suit Contract. Make sure to have a plan and not just start playing. At Notrump, count your sure tricks and figure out how to develop more while considering your stopper situation. At Suit Contracts, realize what tricks you might lose and figure out what you might do about it and decide if you need to draw trumps right away or do something else. For help/review, see "Larry Teaches Declarer Play at Notrump" or "Larry Teaches Declarer Play at Suits."
4) Concentration. The 800-pound gorilla of improving. If you can't focus, you won't play well. If your mind is wandering, you won't play well. This isn't easy -- we all have issues such as poor nights of sleep, medication, aging, etc. -- but commit to at least being aware that you need to try harder to focus, focus, focus -- and avoid dumb mistakes. Logic and concentration are much more important than memory.
Too much time/energy/study is wasted on what is NOT important. Put the things below on the back burner:
1) Don't waste time on conventions. Just know the few basic ones. Make sure you know Takeout and Negative Doubles, Stayman, Blackwood, Transfers -- that's about it. For a complete list, click here.
1a) Don't fill your brain/partnership with fancy methods/agreements. Just know basics. If you come to the table fretting about memory, your brain isn't clear to just play basic logical good bridge. System tinkering (unless you are a National Champion level player) is a recipe for disaster. KISS (Keep It Simple Sweetheart).
2) Some things are just too difficult. Complex squeeze theory. Sophisticated slam bidding (especially in the minors), Specialized conventions like Kickback and Serious 3NT. Sure, to win the Bermuda Bowl, you need to master these things. But to play good bridge, you can survive without them. I am not meaning to "dumb things down." Just being practical. You can't imagine how often I get asked: "How do I respond to Blackwood with a void?" Don't worry about it. It is less than 0.00001% important. And when it does come up, you won't remember anyway.
3) Repeat steps 1 and 1a above. If you are planning to take bridge courses/lessons and the teacher is just spewing conventions, consider a different class (or teacher). IMHO, system/methods are 1 or 2 % of bridge. The other 98-99% is what matters, yet players put way too much time/energy into fancy bidding theory. It is counterproductive to study complex system/conventions. It will make you WORSE -- not better. I see players at all levels having more disasters and poor results (than good ones) due to "system." Your best bet is to adopt CRAFT as your favorite convention. What does it stand for? Well, the first three letters stand for "Can't Remember A ..."
P.S. Counting -- Takes years and years to master. Important? Yes. Be patient. It ain't easy. Start by trying to count just one important suit (likely a trump suit or the suit you are working on).
For a similar article on this topic, see: How to Bust a Slump
For my slightly nasty article on lessons see: How to Get on my Bad Side