Command-Tab switcher.
Command-N for a New Window if you don’t already have one open.
For a more advanced trick, use the Command-Tab switcher, after taking your finger off of tab once the application you want is selected, but before you take your finger off the command key, press the option key, and then take your finger off the command key and then take your finger off the option key. This sounds more complicated than it is but once you get used to it, it’s straightforward and the following behavior will execute.
1. If there are no open windows, the most recent minimized window for that application will unminimize and take focus.
2. If there are no open windows and no minimized windows, a new window will open, as in the Finder, Terminal or Safari.
In an application like BBEdit or TextMate, it will create a new file, and in the case of TextEdit or Pages, the Document chooser or whatever Apple calls this dialog will pop-up. In an application like Notes, the main window will appear.
This all sounds complicated, but if you know your applications well, and what type of application it is, you’ll quickly suss our the pattern that it is basically a Command-N shortcut from the switcher except for some of those newfangled iCloud-aware and/or Database-centric apps.