If you are upgrading to Media Wiki 1.25 or later, you will also need to install some external PHP libraries using Composer or a provided collection maintained for the Wikimedia wiki farm.More details on installing and updating external libraries can be found in the Git download documentation.Within the distribution tarball, or within the files checked out/exported from Git, there are a number of files with capitalized filenames, one of which contains the RELEASE-NOTES (wiki).
After you extracted the files locally, use your favorite FTP client software to upload directories and files to the server.
Extensions that are not adapted should use the old way of installing them. New variables may be added in newer versions, or some existing variables changed their type.
Refer to the installation instructions on the extension's page for more information. We usually try to use sane defaults for them, and in case of type change, be backwards compatible.
Patches are incremental, you can not skip a version. Media Wiki will log warnings if any of them are still found to help you remember.
(You will also need to adjust any custom skins to follow a similar convention.) See Manual: Skin autodiscovery for details.