Homemade salt water taffy
To manually pull taffy, either you can stretch out the taffy between your arms by gripping one end of the taffy with each hand and extending your arms. This is extremely strenuous, and a lot of work especially when the taffy is cold or when starting.

Another option is to get a Taffy Hook, which looks like this:



It doesn't have to be anything specialized, any stainless-steel hook you can mount on the wall or temporarily attach to a surface will suffice. The idea is to hook the taffy on the loop and pull towards you or the ground, re-loop and repeat until the taffy is the desired consistency. 

There are a number of home contraptions in various price ranges that work either by a motorized system or a hand-crank:

Youtube video of a hand-crank taffy puller

There are even homemade taffy pullers that you can find by searching the internet if you are more mechanically inclined.