Logging in
The first time the app starts, it will prompt you to log in by redirecting you to the itch.io website in your browser. You'll sign in to itch.io as usual (including any two-factor authentication you have enabled), then authorize the app to connect to your account via OAuth. Once authorized, the app will automatically complete the login.

A legacy username/password login flow is still available but will be removed in a future release.
Note: It is not possible to use the app anonymously at the moment, although downloading or even purchasing is possible on the itch.io website without an account.
Multiple profiles
You can log in with multiple user accounts from the itch app. Each profile has its own set of browser tabs, has access to its own creations, etc.

However, downloads and installed games are shared between all profiles.