Click 'Create project' and give it any name you want.
If you see a sidebar that includes 'APIs & auth,' click on that. Scroll down to 'Google Maps API v3' in the list, and click the On/Off button to activate it. (It may or may not jump to the top of the list after you turn it on.)
Click on the 'API Access' or 'Credentials' link in the sidebar. If a key has not already been created for you, click 'Create new Browser key...', or 'Create New Key' and then 'Browser key'. You can leave the "allowed referers" box blank.
Your key will be 39 characters long and will probably start with 'AI'.
If you need to retrieve your key again in the future (or create additional keys), just use the 'API Access' (or 'APIs & auth' -> 'Credentials') link in the left sidebar.