If you use QGIS, you have at least two options to publish your maps without dealing with a server: install qgis2web-Plugin and generate web-maps with openlayers or leaflet: - you can upload the output to a webspace (if you have one) and your web-map is there. However, export tries to "translate" your QGIS-project as good as possible to openlayers/leaflet, but many details (styling etc.) that work in QGIS will not be rendered in the same manner. So if it is just for publishing some basic maps, it's good enough. If you know how to adapt the output, the export could be a start and the final styling can be done there.
Second option and probably the fastest and least complicated way: QGIS Cloud - they have their own webspace you can use: just upload all layers as well as your QGIS-Project with the qgiscloud-plugin and your webmap will appear on their site in the exactly same look as your local QGIS-project. You don't need any understanding of web-technologies - when you have your QGIS-project ready, just press a few buttons, that's it. Basic use is free, additional use of webspace with costs.
Of course, you could also use QGIS server: but then, you have to install/configure it on your own.