Hi I'm going to Katowice next week and will take a taxi around 1:30am.
For the safty reason, I should have at least some basic knowledge about identifying a "real"/trustable/good/legal taxi or a taxi driver.
Do they wear uniform or something?
They do not wear Uniforms.
The car will have a sign saying Taxi on it.
If you are worried you should take the registration number of the car and give it to a friend or someone you trust.
But you ought to be fine, ring one of the taxi companies and make an appointment to get picked up.
yes, that's the best idea - ring the taxi company (remember the company name!), they will ask you where you are and maybe what's your name (in case there is a lot of people waiting for a taxi in that area). then wait for the taxi with right sign on it, and tell your name to the driver
I gave you full explanaition to avoid confusion - that's all those small things that always scare me abroad ;)