For me, it started with Autocross.
I recommend that as a starting point for anyone interested in doing track events.
It is a natural progression without the big up front costs.
It is also a great learning environment. AX teaches you all of the basic fundamentals of car control and handling at speed, but in a very compressed time frame.
The old adage is that good autocrossers make GREAT road racers. It doesn't always work the other way around.
Tpyically, at an AX event, there is discussion about upcoming HPDE events and local club track days. You can also visit the web sites of local clubs for their list of upcoming events.
A good all around resource for AX and track events is
That can get you pointed in the right direction as well.