I have a trailer almost exactly like that.
Take a look at this link: [uri]http://www.amazon.com/Coupler-Attachment-InStep-Schwinn-Trailers/dp/B0013TR66I[/uri]
The trailer should have come with the parts shown in the link. The black part should be put on your rear wheel axle, on the left side, going through the small hole on the black part. I typically leave the black part on my bike all the time, even when the trailer isn't hooked up. On the end of the trailer's bar that comes forward, there should be a flexible spring, followed by a cylinder with a hole going through it. You put the cylinder in the large hole of the black thing, and the hole going through it should line up with the hole going through the black thing. Then you put the silvery pin part all the way through at hole, and the curved attachment to the pin goes around and hooks over the end of the pin. This is quite secure - the strap is only a failsafe.
Let me know if this description isn't very clear - I can post some step-by-step pictures when I get home if need be.