I can design but I am new to the "phone app" world. How do I make an awesome logo for this smartphone-app job? I am looking for a "To Do" list, please.
To create an iOS icon, you simply have to provide images for at the various sizes. For iOS, the main sizes are (if you're making an iPhone and iPad app):
For Android, the image sizes are:
Icons are delivered as PNG files. Generally speaking, you do need to provide all those sizes (they're used in different places throughout the OS). If your app uses documents via iTunes, there's a few extra sizes.
In terms of the actual icon, that's something you'll have to figure out for yourself. A lot of to do lists use a tick. Do you want to fit in or stand out?
If you'd like to be inspired, Dribbble is a great place to start. Please note that I said "inspired" — make sure your icon is different to other icons you're inspired by.
I started another question that might be useful to you, regarding workflow for building the various sizes.
Apple have some good advice for iOS icon designers: Custom Icon and Image Creation Guidelines.