Hi Craig - We all have to start somewhere, so don't feel bad about asking the question. At least you know what a headstock is, so that put's you way ahead of most of the population! :biggrin:
Anyway, the spindle on your lathe is threaded on the outside to accept chucks, faceplates and such. The inside of the spindle should have a taper to it. A "Morse Taper". Your documentation should tell you whether it's a #1, #2, #3 or whatever size taper. #2 is very common and that is the size mandrel that is offered in the package you linked.
You just push the end of the mandrel (the end with the Morse taper) into the spindle and friction holds it in place for turning (supported by a live center in the tailstock).
If your lathe doesn't have a morse taper in the spindle, then you would need something else.
I would encourage you to consider doing a little more research before spending $100 on that package. Carbon steel gouges will take a very fine edge, but the edge is not as durable as HSS (High Speed Steel) . Carbon steel can also be "ruined" if you get it too hot while sharpening on a grinder. (Google "carbon steel losing temper"). Which raises the question "How do you plan to sharpen your tools?". Sharp tools make all the difference in success in turning.
The package you linked isn't bad. You just might be able to do better for the same or less money. Consider asking for alternative recommendation on the forum here.
Good luck.
Ed