This depends almost entirely on what exactly you are hosting. Is it a Node.js app? ASP.NET? Windows? Linux?
In Visual Studio it is more-or-less as simple as right-clicking a project and selecting "Add -> Docker support": https://learn.microsoft.com/en-us/dotnet/architecture/contai...
In Azure DevOps pipelines or GitHub Actions, it's also quite simple to add a container build step: https://learn.microsoft.com/en-us/azure/devops/pipelines/eco...
In the actual Azure subscription you just need to create an Azure Container Registry resource to host the image. I believe you can also use Docker Hub, if you prefer.
Then in App Service just host the container image instead of the raw code: https://learn.microsoft.com/en-us/azure/app-service/tutorial...
That should be about it. The effect of this is to "zip up" your loose 'js' files (or whatever), making deployments much faster. The build happens before this step, so the container image is "final" and will run directly without needing any npm steps or whatever at deployment time.
If you need something like hot-reload or similar very fast deployment times, then App Service is probably not the right environment for you. However, with containers its often possible to have a fast local deployment edit-build-test loop and then have the same environment running in production. This is the main benefit of containers!