Common advice to those seeking ways to improve their driving is "get more seat time". In other words, practice, practice, practice. Fine advice if one has a way of knowing where there are opportunities to improve. As they say, doing the same thing over and over and expecting different results is insanity!
To improve, one has to have measurable goals and sub-goals and a means of getting some feedback. All too often, drivers have just one goal, to go faster.
The best way to improve is to get a coach or enroll in a driving school.
When it comes to coaches, you generally get what you pay for so keep that in mind when using a free coach; the quality varies greatly so don't stick with just one coach. Excellent coaches are not cheap, but the results will improve driving skills and reduce lap times much more than spending it on that cold air intake or "free flow exhaust" you've got your eye on!
There are many driving schools to choose from and many have been reviewed. Attending schools that are complementary is a great way to expand one's repertoire. Off-road rally, drifting, and snow/ice driving schools provide new/extreme scenarios that are complementary to road racing skills, as an example.
Next best way to improve is to use tools and resources to provide useful feedback, pointers and goals.
The single best resource on the planet is almost certainly Ross Bentley's Speed Secrets which encompasses books, videos, and coaching. I've found the Inner Speed Secrets books invaluable, however, they are aimed primarily at race car drivers. His book on High Performance Driving is likely more suitable for the HPDE/lapping day driver just starting out. For anyone with some experience on the track, his Ultimate Speed Secrets is likely the best choice.
I've also found these books very useful:
Using lap times as the main feedback is like getting a test score without knowing which answers you got right or wrong! Yet so many drivers never go beyond just looking at their lap times and gut feel about what they can be improve in their driving.
Augmenting lap times with video can be useful for reviewing driving line, steering and throttle inputs (by listening to engine/exhaust). The camera should be mounted so it captures steering inputs and behind the driver to also see the track ahead. This can be achieved by using a suction cup mount on the inside or outside of the side window behind the driver; or on a roll bar.
Data acquisition systems range from phone apps to dedicated mid-priced systems (AiM, Race Technology) to complex systems (Race Logic and Motec) costing thousands of dollars. Each of these systems includes a data analysis (visualization) application to make sense and meaning of the data. An alternative is to use standalone analysis tool such as Track Attack which is capable of importing data from most of these systems. Track Attack also supports virtual racing applications Assetto Corsa and iRacing which is great for comparing real world data vs virtual.
While getting the maximum out of data analysis can be a bit time-consuming, one can get a lot from quick glance at the speed graph to spot areas of inconsistencies between laps. The time slip graph clearly shows where time is gained/lost. Comparing data with other drivers is one of the best ways to find areas of improvement. CMS Lap Timer makes it easy to share data at the track via AirDrop and Bluetooth Exchange.
Two excellent books for diving deeper into data analysis are “A Practical Guide to Race Car Data Analysis” and “Analysis Techniques for Race Data Acquisition”; not cheap but worth the investment.
Finally, keep the ego under control and try something different :)