Quote Originally Posted by boolBoy View Post
We should have: a server with a database, and 2 PCs with applications, which allow to add, delete and update entries in the database on the server (local network).
This is a very classic and common problem. Just set up a MySQL server (or something else). Read the documentation carefully on how to set it up and protect everything.
Really learn how to use SQL.

As for the programs themselves, Qt allows you to easily connect and work with the database. See the QtSql module for documentation and examples.

What do I have to know in order to cope with the task?
Apart from what I already said above, this is a too easy question to answer with an insult, so I guess I leave it with a comment to use common sense.

..., but I really can't struggle to cope with everything at once, ...
It's "struggle with" or "can't", not both as that would be a double negation.

You start with the basics: how does a computer work.
Then you can start with basic C++
If you have a decent knowledge of computers and C++, you can start with Qt

Just do not expect to do this in one day.