I've always felt like the improvement was truly gradual, but what smutz said is really important... identify and break bad habits. Some very common bad habits I had to learn to break:
1. Stop 'englishing' in cuts with sidespin. Some people love to just undercut every ball and use outside english to throw it in. Others do the opposite and use inside. Some players absolutely cannot make a rail cut without low outside english, if they had to make it with center ball or inside they're helpless. Learn to make a ball with no english and then use the correct english to position the cueball, seldom will you use english just to help you sink a ball.
On the same track, if you find you can only make a certain ball by rolling it in or slamming it in, try your hardest to learn to make it at all speeds. Some players feel like you have to power long shots for example, and even though speed will help prevent a shot from rolling off, roll off is really only a concern at waaaay too slow speeds, at least on my local tables.
2. Stop using 'tricks' and 'body english' to move the cueball. Don't snap downward or jab at your draw strokes, don't twist the stick sideways on shots that need sidespin, don't start your stroke aiming at one spot and then move up or down or sideways mid-stroke to correct it (which a lot of people do subconsciously).
3. Don't be lazy with your leaves... pick a spot beforehand on every ball, don't just fall into patterns and figure "any angle is fine, it's an easy shot". Don't assume "the odds of getting totally straight here are slim, I should be ok"... make SURE you're not straight. Pick a particular leave area (really an exact leave 'spot') and try to put the cue ball there. Do this on every shot, and do it before you get down to shoot.
4. Don't fall prey to wishful thinking. This is a huge problem and ties in with 3 (anyway it was a big problem for me). Don't try to 'hold' a ball when you can sense it'll be very tricky... if a cut is steep and you'll be forced to send the cueball across the table, then bite the bullet and do it, don't just try to shoot extra soft and baby the OB in and hope you can get the leave. If you can see you're too straight to move the cueball the way you want, even after cheating the pocket, you must consider playing it another pocket, banking, going railfirst, or playing safe... don't just ram the ball extra hard and pray it works out, because it won't.
Other examples of wishful thinking -
...You can see an object ball just baaarely can NOT pass another ball, but you talk yourself into thinking it can. Or you can just see enough of a ball to hit it (but not to make it) but you convince yourself you can make it.
...You know you ought to check to see if a ball can pass in a tight situation, but you're too lazy to walk around the table and make sure, and you just shoot as if it definitely goes.
...You know you'll be in trouble if you leave the cueball parked on the rail, but you can't make yourself use the added force or spin or whatever that's needed to prevent it
...You can see a cut is too steep to send the cueball into a particular area but you try anyway (like the cueball is definitely going uptable when you're making a sharp cut along the short rail... but you try to hold it on your side of the table)
...you can see a certain ball is really important for getting a breakout or falling into a tight position, but you shoot it 'early' anyway without using it the way you wanted because it's the easiest shot and you're scared of missing the other available shots.
... you know that playing a very very sharp cut in the side is nearly impossible, and it'd be better to play such a shot in the corner (or to bank it) but you try anyway.
5. KISS - don't automatically play every ball in the nearest pocket, if it means you need to move the cueball a lot more to get position on that shot.
Once you understand english and have decent fundamentals, thinking and work is what separates you from other players. Try very hard to play every shot correctly even if it means taking more time, or making the shot harder, or taking a more difficult option, etc.
Also, be ready to go backwards before you can go forward. If the correct way to play a shot is with inside english to get position... but you only know how to make it with outside english, use the correct (inside) english even if it means missing something you are sure you could have made with the wrong english. In the short run you may miss more and lose more but in the long run you'll get stronger and eventually master making the cut with any english, and will start winning again.
