So, I’ve downloaded a fresh DietPi image and I’ve put it on my SD card.
I eddited dietpi.txt in the boot partition and set a static IP address.
When everything was done, I wondered why apt-get update was getting so slow, so I looked in /etc/resolv.conf and there is a local IP address above (192.168.1.11 something like that). That is obviously not my DNS server, so I’ve changed it.
There was no option in /boot/dietpi.txt to enter the DNS server, so please add it or use 8.8.8.8 as DNS server instead of 192.168.x.x.