Visual Studio Code IntelliSense suggestions don't pop up automatically

To activate IntelliSense on a .NET project:

1. Open project folder: File->Open folder...
2. Click on the flame on your bottom left corner, pick your project
3. IntelliSense activated!

From what I've seen, IntelliSense cannot be activated on a .cs file alone. (See @natemcmaster's answer).

OmniSharp doesn't know where your project files are. In your screenshot, the left sidebar says "You have not opened a folder". OmniSharp will look in your currently opened folder for project files.

1. Add your folder. File > Open Folder...
2. Make sure you have a project file (either project.json or your *.csproj files).

This should be enough for OmniSharp to start providing you Intellisense.

You just have to pick up the language type from the bar at the bottom (the button with the flame).