If you need to access your volume's data, you should first check if there is a container to do so. For example if it is about MySQL data you should check the official phpmyadmin container, add it to your project and start it if needed.
However, if you just need access to plain files, go to Manage => Volumes. Start the filebrowser for any volume and it'll open in a popup (give it a few seconds to start). There you can up- and download files.
Keep in mind that the filebrowser is not meant to be for big file up- and downloads. Changing anything in a running container is an anti pattern for microservices anyway. Your service should be able to run from scratch when you start it without need for uploading files and other changes.
Tags: filebrowser, filemanager