The springer fork you have in the link look to be a threadless style. The part of the fork that goes through the head tube of the bike frame is called the steer tube. These come in two flavors: Threaded, and threadless. Now the threaded forks are usually 1". Threadless are usually 1 1/8". Some bike frames might be sized in such a way that you can swap out the headset from threaded to threadless. The headset is made up from many parts. The crown race goes on the steer tube right where it meets the fork legs. This part of the fork is usually machined so the crown race can be tapped on. This part of the fork needs to be measured to make sure the right size crown race is available. They make crown race setting tools which is usually a steel pipe with an aluminum sleeve on the end that contacts the steel crown race and allows it to be set with a hammer without damaging it. The next part will be the lower bearing. These come as sealed units or loose balls in a cage. Next parts are the lower bearing cup and upper bearing cup. These parts will be sized to fit the head tube of the bike frame and the steer tube of the fork. They are also pressed into the frame. Again, they make a press tool that does this. I have used a piece of all-thread and an assortment of washers with success in the past. Next is the upper bearing which comes in the same flavors as the lower bearing. On top of that will be an upper bearing race, then a wedge of some kind then on threaded forks, there will be a nut that tightens on the upper race which is also threaded. For threadless, there is a star nut that is pounded down into the steer tube then the stem and any spacers goes on then a stem cap on top of the entire works is tightened down until the headset moves without any excess play. Then the stem bolts are tightened. It is these bolts that hold the entire works together. On threaded forks, they use what is called a quill stem and a wedge and a bolt hold the stem in place.
This is the part on that particular Huffy frame that will limit what you can do. I don't believe that headtube on that frame is big enough to take an 1 1/8" threadless steer tube and headset. What you need to search for is 1" threaded springer fork. This "should" be able to replace your current fork making use of the existing headset and stem.