Writing C# in Debian

What do I have to install?

apt install mono-mcs

and optionally

apt install monodevelop

if you want something more like an IDE.

mcs is the compiler. You can run the compiled program with mono prog.exe (or as ./prog.exe with binfmt_misc support enabled, which I believe Debian will do by default).

Is there something like a prompt where I can try running snippets of code?

apt install mono-csharp-shell

and then

$ csharp
Mono C# Shell, type "help;" for help

Enter statements below.
csharp> Console.WriteLine("Hello world!")
Hello world!
csharp>