Run hugo shell command. In VSCode run Command Pallete -> Run tasks -> Build site.
Or press command + shift + b (control + shift + b for Windows and Linux) for select task in Build menu. If you setup Default build task command will be run without showing menu.
Serve site
Two possibility :
Run hugo server shell command to start like final site.
In VSCode run Command Pallete -> Run tasks -> Serve site.
Run hugo server --buildDrafts shell command to start site with draft page.
In VSCode run Command Pallete -> Run tasks -> Serve draft site.
Commands in Command Pallete
version - show local version of Hugo.
remote version - show remote version of Hugo.
create content - create content in content/ directory.