I guess you can kind of look at it on the macro- [big-picture] and micro- [more detailed] level.
Macro, the heading of the ILS will give you a good starting point, for example, the westbound runways at KLAX are 250°, so you know your heading will be around there.
However, if you start 10 miles away and set your heading to 250, the chances of you landing on the centerline without any correction are virtually nil.
So, as you get closer to the threshold, making sure that centerline deviation indicator (CDI) stays directly in the middle, and to do that, you’ll have to make small manual corrections. The closer you get, the more small changes will affect the indicator. Minor adjustments are less important 10 miles out than the last mile, for example.
But you definitely need to keep that CDI in the middle, and AP (without APPR) will very rarely accomplish that. Now, you can still use AP along the way, but you’ll need to make manual adjustments at some point, and it becomes more important the closer you get.
When the CDI is flashing, it just means that you are farther afield of the centerline than the threshold for the indicator. So, if it’s flashing on the far left, you need to make quite a large swing over to your left to catch the localizer. When the CDI stops flashing, you’re getting closer to catching the localizer, so you know that you are getting close® to the centerline. When the CDI is in the exact middle, you’re on the centerline. Anywhere else, and you’re either left or right of the center line. If you’re on final and the CDI goes from solid to flashing, you’re in trouble, as you’ve deviated quite a ways from the center line.
What generally should happen is that, say you’re on approach and given a 30 degree intercept, it will start flashing, then become solid and start moving toward the center, when this happens you’ll want to turn to that heading that you’ve been trying to use, and timing it such that you hit that heading right when the CDI is directly in the middle. That’s intercepting the localizer.
That will get you close, as stated before, but manual adjustments should be made along the way to keep that CDI in the middle the whole way.
10 miles out, if you still want to use AP as much as you can as you learn to control other things, you can make one-degree adjustments to AP heading to get the line back in the middle. But the last few miles, you’ll definitely have to go manual at some point, with maybe some rare exceptions where everything is just right, to make sure that you touch down on the centerline.
It just takes practice like anything else.