Originally posted by neon_duke
Well, you have two ideas kind of stuck together in you head, and they don't necessarily relate directly.
Late braking is just what it says. Clear enough.
Late apex, though, just means you touch the apex of the turn after the midpoint of the corner. Early apexing means you touch it before. But that doesn't relate directly to your braking points.
What you want to do is brake early and apex late. This allows you to get most of your rotation done early in the corner, so that the later part of the corner is done on as gentle a curve as possible, allowing you to accelerate more and exit the turn faster.
What controls are you using? The buttons were way too hard for me to get any sensitivity with, so I switched to having the right analog stick be gas/brake after about 1 hour of playing, and never looked back. Sometimes it's better to coast through the apex, or to feed the throttle in slowly, to avoid spinning.
For a suggestion, try this for practice. Buy an RX-7 RS, put T2 tires on it, but don't make any other mods. Then practice at SS R5. Most of the turns there are simple, with a few combinations, and the walls make it easy to judge your track position. Concentrate on being smooth and avoiding tire squeal.
As you approach a turn, get as far over to the outside as you can, and keep one eye on the gear indicator. There is a little number next to it, which is the suggested gear for the upcoming turn. That starts to blink at the braking point for the next turn. Practice braking when the light flashes, then feeding the throttle back on as you turn in. You should be able to accelerate through the inside apex and let the car track out toward the outside wall again. When you get the line right, you'll be amazed at the speed you can carry.
Good luck!