I figured it out finally. Thanks to Matthias Kuhn for assistance.
First one needs to create an attribute form ("Attachment", used to be "External resource") for a layer field in question. This will enable camera function once in Qfield. Open properties-dialog of your layer to accomplish this.
Once you're working with Qfield, be thoughtful about saved paths of taken pictures: you have to choose between file paths and directory paths. In case you transfer manually your pictures from your mobile device to PC, your directories will change thus I myself chose to save file paths.
What I didn't yet find out was, how to save pictures directly to a server.