We used to run a social website, on a standard LAMP configuration. We had a Live server, Test server, and Development server, as well as the local developers machines. All were managed using GIT.
On each machine, we had the PHP files, but also the MySQL service, and a folder with Images that users would upload. The Live server grew to have some 100K (!) recurrent users, the dump was about 2GB (!), the Image folder was some 50GB (!). By the time that I left, our server was reaching the limit of its CPU, Ram, and most of all, the concurrent net connection limits (We even compiled our own version of network card driver to max out the server 'lol'). We could not (nor should you assume with your website) put 2GB of data and 50GB of images in GIT.
To manage all this under GIT easily, we would ignore the binary folders (the folders containing the Images) by inserting these folder paths into .gitignore. We also had a folder called SQL outside the Apache documentroot path. In that SQL folder, we would put our SQL files from the developers in incremental numberings (001.florianm.sql, 001.johns.sql, 002.florianm.sql, etc). These SQL files were managed by GIT as well. The first sql file would indeed contain a large set of DB schema. We don't add user-data in GIT (eg the records of the users table, or the comments table), but data like configs or topology or other site specific data, was maintained in the sql files (and hence by GIT). Mostly its the developers (who know the code best) that determine what and what is not maintained by GIT with regards to SQL schema and data.
When it got to a release, the administrator logs in onto the dev server, merges the live branch with all developers and needed branches on the dev machine to an update branch, and pushed it to the test server. On the test server, he checks if the updating process for the Live server is still valid, and in quick succession, points all traffic in Apache to a placeholder site, creates a DB dump, points the working directory from 'live' to 'update', executes all new sql files into mysql, and repoints the traffic back to the correct site. When all stakeholders agreed after reviewing the test server, the Administrator did the same thing from Test server to Live server. Afterwards, he merges the live branch on the production server, to the master branch accross all servers, and rebased all live branches. The developers were responsible themselves to rebase their branches, but they generally know what they are doing.
If there were problems on the test server, eg. the merges had too many conflicts, then the code was reverted (pointing the working branch back to 'live') and the sql files were never executed. The moment that the sql files were executed, this was considered as a non-reversible action at the time. If the SQL files were not working properly, then the DB was restored using the Dump (and the developers told off, for providing ill-tested SQL files).
Today, we maintain both a sql-up and sql-down folder, with equivalent filenames, where the developers have to test that both the upgrading sql files, can be equally downgraded. This could ultimately be executed with a bash script, but its a good idea if human eyes kept monitoring the upgrade process.
It's not great, but its manageable. Hope this gives an insight into a real-life, practical, relatively high-availability site. Be it a bit outdated, but still followed.