I have a somewhat older printer and wanted to find out whether it can be connected to my cell phone, but I can't find anything on the internet.
It's the printer: Kodak ESP 5250
Does anyone know if that works? And if it doesn't work, is it possible with a USB stick and laptop?
That doesn't work, or not with an older one. It is true that modern high-end printers, which may have bluetooth, can be connected directly to a mobile phone to print photos, but this is only an exception and not a printer standard.
If so, the printer and mobile phone are connected to each other in a home network, but even then you have to use another device, e.g. Tablet, laptop or pc; or use the detour of a USB stick to run the documents to be printed over it.