I think you can reasonably assume that the 2 thin wires are the primary. If you know the original primary voltage then it is reasonably easy. Just connect the primary to its intended voltage and measure the secondary end to end and end to taps.
If you don't know the primary volts then you have a bigger issue. If you have a variable supply then you can feed it at variable volts with an ammeter in series with the primary and increase volts, watching the ammeter.
I assume you are in N.America so it is likely to have been 110v or 220v. You should get to 110v with only a modest primary current. If it was intended for 220v you will get to 220v with modest current. If it was intended for 110v, when you get to about 130v the primary current will shoot up and you will then know that it was 110v. If primary current goes beyond about 2A then you are saturating it.
If you don't have a variable supply then it is safest to assume that it is 110v. It may have been wound to charge several voltages as well as having taps for charge current.
Possibly it may have been intended to charge 6, 12 & 24v batteries. You may be able to make some sort of guess when you have secondary voltages. for 6v you will have something 7 & 9v. for 12 then perhaps 13 to 16, for 24 perhaps 25 to 30v. If the original rectifier was an old selenium or copper oxide device the volts may be a little higher.If your lowest voltage tap is well below 6v then it may be reasonable to suspect that the primary was 220v. Without a variable voltage supply the safest thing to do if it looks to be 220v is to feed the primary through a large 220v load and measure the primary volts. If it is 220v then the transformer will have near 220v across it and the load very little. If most of the volts are across the load and the transformer has only about 130 then it will be 110 primary.
This is a bit hit and miss, if you are sure what you are doing it will work, but if you are not really sure what I am on about then You had better assume it is 110 and hope you have suitable taps for your needs.
It looks as though it is old so it may be class A rated so don't run more amps than will bring its temperature beyond where you can stand your hand on it after a long run.
I suspect it will not give much over 20A long term rating but you will only find out when running it.
Flux