Hello,
I am working on a project where I will need my Arduino UNO with Ethernet Shield to be connected to LAN.
I have already a working code for establishing a telnet server on my Arduino UNO.
But unfortunately my project manager just told me I should not use telnet. 
So my question is what other possibilites can I use for receiving and transmiting data to my UNO?
I am fairly new to LAN and Ethernet Shield issues... Can I e.g. create some website "chat" or sth?
Thank you 
But unfortunately my project manager just told me I should not use telnet.
If that is because of a security issue, the Arduino library does not support any encryption methods like https or ssh. If you are going to expose this device to the internet and control any type of sensitive devices (like your home or business security system), then you should use a device with more horsepower than an Uno.
I suspect that telnet is too simple for the project. You could ask and see if HTTP will suffice?
HTTP is supported the Ethernet library.
What is required for HTTP?
I mean I have no http or web skills. Is there any code for a simple http page to type in some values that are transmitted to the Arduino Ethernet Shield and vice versa?
Or how can I get access to my Arduino UNO via HTTP? Correct me if I missunderstand this: I believe HTTP uses a "web page", doesnt it?
You are correct about http serving web pages.
There is already and example of how to use it in the Ethernet library. It loads a simple webpage that you create on an SD card. Its really straight forward. Took me about 10 minutes to get up and running about a year ago.