https://marketplace.visualstudio.com/items?itemName=jebbs.plantuml
https://www.codeproject.com/Articles/1278703/UML-Made-Easy-with-PlantUML-VS-Code
The VS Code extension makes use of the PlantUML server at http://www.plantuml.com/plantuml so installing your own server is not normally required. If you do choose to install the server the Docker is recommended.
docker run -d -p 8080:8080 plantuml/plantuml-server:jetty
See https://github.com/plantuml/plantuml-server for more details.