For the datasets, I tried to access (like the full disc image in visible wavelength, MTG 0 degree), it is sufficient to register at eumetsat to get a username and password. The eumdac python tool is probably the easiest way to access the data:

https://pypi.org/project/eumdac/

(If you do not want to use python, the --debug option is quite useful to see exactly the request made. The output is either some JSON metadata or a large zip with the netcdf data)

Read the data store user guide. You have to register.