Another question about proper input voltage of a high voltage transformer

I know that the output voltage is supposed to be 3.1kv.
The input voltage is supposed to be either 110v or 220v.
How do I find out without causing any damage?
Note: I am generally uneducated about transformers.

Well 3.1KV is dangerous in any case. Be careful! But here are some options:
1. connect it to 110Vac and measure the output with an appropriately safe instrument. If you get the expected 3.1KV then 110VAC it is. If the primary is 220V then you will only see 1.55KV.

2. Connect 110V to the 3.1KV side and measure the "primary" voltage. If you get 110* 110/3100= 3.9VAC then 110VAC it is. If you get 110* 220/3100 = 7.8VAC then its 220.

You really shouldn't mess with even 110V unless you know exactly what you are doing. I take no responsibility!

Your transformer has 2 primary windings. If you connect them in parallel, the primary voltage should be 110 volts. If the 2 windings are is series, the primary voltage should be 220 volts. There should be a schematic on the transformer showing which terminals connect to which windings. Connect them for the voltage you have.