As Umbraco 15 runs on .NET 9 you must have the SDK installed on your machine. This can be installed through Visual Studio, or direct download on the .NET website.
go into src
run npm ci
run npm run dev
This will build the typescript, output it into the folder within the Umbraco 15 website for use in there, more specifically: /examples/Umbraco15.Website/App_Plugins/Example.UI/scripts.
In a separate terminal window, to run the umbraco project, open the path /examples/Umbraco15.Website/
run dotnet run
You can then launch the umbraco solution and should see the new back office section.
Note
For a more general introduction into getting started with development for v15, please read the Umbraco Documentation