To implement caching in Azure App Service, you need to configure the Cache-Control header specific to the technology stack of your application.
For ASP.Net applications, this can be done in the web.config file, for PHP applications , it can be set in the htaccess file and for Node.js applications, you can use middleware to set the header.
Each technology has its own method for configuring these headers, so refer to the relevant documentation for your specific stack to set the Cache-Control header to max-age=31536000 for caching static assets effectively.
It is interesting to note that Azure App Service support Local Cache in many scenarios, that can be enabled by you to improve the performance. Refer: https://learn.microsoft.com/en-us/azure/app-service/overview-local-cache