Since the release of Google Maps API for Flash, I wanted to start incorporating this free service in my apps as I've seen a lot of good examples being built around. One thing to take note is this ActionScript API will only work in Flex and not in your usual Flash app.
Google API Key
Before you can even start coding, you need sign up for an API key so you can use their free service. Get the key here. You can get as many keys as you want using only 1 Google account. That being said, let's get 2 keys instead - 1 for your site (http://www.mysite.com) and 1 for your local development server (http://localhost). This makes testing much faster rather than you constantly uploading files to your production server.
Google Maps API
Download the Google Maps API for Flash (Flex) here.
Next, unzip this archive file and you'll see docs and lib folders. Inside the lib folder, there exists the map_flex_1_3.swc Flash component. Drag and drop this to the "libs" folder in your Flex project. Now you're ready to code.