be80be is correct. You need to connect the SSR +ve to +12V, the SSR -ve to the transistor's collector. The transistor's emitter connects to ground. The base connection is fine.
But before you do anything else - There are a great many sellers peddling counterfeit Fotek SSR-40 and SSR-25 solid state relays, and these SSRs are known to burst into flames.
The fact that your's has ratings for 3-32VDC, yet won't even switch with 5V applied indicates that it could possibly be one of the counterfeit items.
I'll see if I can find the article I read a short time ago, that has pictures showing a real Fotek SSR and a counterfeit one. From memory, it wasn't too hard to tell the difference.
Edit: Just looking at the pictures, on close examination your's looks very much like a genuine Fotek SSR, except that at the bottom right corner of the indentation that holds the label, a real one doesn't have a sharp 90 degree corner in either the plastic or the label, it's 45 degrees on both.
On the pic you showed, the label has the 45 degree corner, but the plastic casing doesn't.
Otherwise, your's definitely looks more like a real one than a fake.
It might just be a good fake, though, so I'll leave it up to you to decide. Apart from that small detail, it looks OK, but if I were you I'd watch it very carefully at first.
Here's the link to the UL warning:- UL warns of solid state relay with counterfeit UL Recognition Mark