Today I logged into my umbraco site and noticed the "click here for upgrade". It led me to download the latest version of Umbraco software in a single zip. UmbracoCms.7.2.8.zip. I never did an upgrades for CMS before, so it felt a bit risky to change a software, when web site already has a content. But it turned to be very easy. It happened in this order (not necessarily a completley correct order):
The site seems to be in working condition now, and I have a good feel and hope that future upgrades will be as easy.