The first time I got this little piece of coiled metal years (and years!) ago, I just scratched my head and went, "huh?". Now what? Searching through all my research stash I stumbled upon a very brief bit of instructions. So, let me help you avoid my initial reaction of disbelief (right! how will that thing fit on my machine?)....
There are now two methods I use, depending on the type (or quality?) of metal used to make the spring. Some are more flexible than others.
See that little circle of metal at the very top of your darning spring? Let's call this the "hooked end" and it does fit around your needle clamp.
Take some tweezers or pliers and try to spread it open a bit. Does it open easily? If it does, then try the first and easiest method.
Slide the darning spring up and over your needle. When you have it one, use your tweezers or pliers to put the hooked end over your needle clamp. Grab those pliers and place on the hooked end, and pull - straightening it out a bit, and sliding it around your needle clamp.
Some of the darning springs have a 'heavier' metal and just won't easily bend over the needle clamp. Those I will put on differently.
Take off the needle clamp and your needle. I use my heavy tweezers to help bend and attach the darning spring. I work on the area the stiletto is pointing to - the hooked end.
The tweezers will help you widen the hooked end opening if necessary. For my machines, I need to make that opening just a little bigger so it will slide onto my needle clamp.
After inserting onto the needle clamp, now begin screwing the needle clamp back onto your machine. Before I tighten in fully, I replace my needle. Tighten it fully and you are now ready to use your darning spring.
After doing this process once, the next time you use the darning spring, it will be the correct size for your machine and you will be able to add it quite easily.
Happy Sewing & Quilting