Are you running on Windows? When you close Todoist it stays running in the system tray (beside the clock) and that is how you can re-open it, by double clicking or right clicking.
Thanks Brendon - - - I found it! I am running on Windows. Now, I want to install it on my Android HTC One phone. I assume I must go to the apps available thru my phone to do that.
Yes through the PlayStore, or you can follow our link, which does the same thing. http://todoist.com/android