Getting started
Install ILSpy extension from Visual Studio Marketplace. On installation Visual Studio Code might ask to additionally install .NET Install Tool for Extension Authors, which is by design and intended.
On first start a .NET runtime is automatically downloaded in the background. This is necessary to access ILSpy decompilation engine.
The runtime is installed into a local VS Code directory and doesn't alter your system. There is one exception: On Linux systems this process might also install some dependencies of the runtime, which could involve adding/updating some packages.
After successful start you will see new "ILSpy" commands in VS Code's Command Palette (Ctrl+Shift+P):
You can either select an assembly file present in your workspace or choose any assembly file on your system. After selection the assembly will be shown in a new Explorer view "ILSpy Decompiled Members":
The tree view allows to explore the namespaces, members and types of the assembly. Click on an item will decompile the member on-demand and show it's C# or MSIL code in an editor view.