How are flyover sequences shot?

Shots like this used to be prohibitively expensive because they required helicopters. Now, amateur filmmakers can use miniature helicopters with HD video cameras mounted on them. The results are pretty great! You would need to make sure that the video quality and color matches the rest of your film, of course, but you can fix a lot of that in post production.

With an rc copter, you'll need to consider the range of the rc signal. Wind and weather conditions affect a tiny, lightweight rc craft much more than a heavy helicopter too, of course, so your shot may not be as smooth.

Planning is also important. With the aerial shot in Shawshank Redemption for example, the camera had to watch the bus, then the prison, then the inmates in the yard, then move around to a nicely framed shot that captured the bus again. That takes a lot of coordination. As with many amateur shoots (my own included!), the more time spent in pre-production and planning, the more time and money you can save on the day of the shoot when you have cast and crew on the clock. However, if you're just shooting nature shots like lakes and forests, you might accidentally get some gorgeous footage by experimenting and not planning too strictly!