You'll then be prompted to sign in or create an account. Just wait, eventually the application will open depending on how decrepit your computer is feeling.
Once installed it will typically go through an automated update at the same time. Once you’ve selected your language and install location it actually installs it. I typically use C:\ Programs\ Launcher or D:\ Launcher because of the UAC complications you can encounter otherwise. The default file path is C:\ Program Files (x86)\ Launcher. It will prompt you to select your language and the next screen asks you where you want to install it. The publisher should be verified and should be Zenimax.
The new Creation Kit for Skyrim: Special Edition is available directly from rather than through Steam but is a little trickier.
How to install and set-up the new Creation Kit for Skyrim Special Edition