There are multiple ways how you can get ASP.Net running on Ubuntu. The classical way would be installing .Net Core and ASP.Net 5 by hand inside a virtual machine. This is handy if you also want to develop on Linux. Coming from Windows, using Visual Studio as my daily driver, changing to Visual Studio Code on Ubuntu is a new interesting development experience.
If you just want to have a server for testing and hosting your stuff I recommend using Docker.