Does anyone have an idea how to scan over a home network or have documentation about this? I can't find a good sollution.
It's a Officejet 7310 All in ONE capable of network scanning and printing on a windows platform
Have you checked with HP's support for that model?
It appears you'll need either the HP Director or HP Solution Center software, depending on age of the machine, and which Operating System version you're using.
The above link explains where to get them, and how to use them.