Search for an available tool at any of the sources you have enabled (that you have not necessarily installed)
winget search <appname>
winget install <appname>
Note that "locally installed" means -- installed on the current computer and available to the current user. i.e. What npm
would call "globally installed".
winget list
Note that you don't use "*" or "?" to search for matches -- just type partial words, e.g.
winget list edge
Will list any locally installed package with "edge" in the name.
winget upgrade <appname>
winget upgrade
winget search linq