Printer Setup, Software & Drivers

I have read many of the previous posts on this related topic and they either don't apply to me or are outside of my printer-education level. 

I have moved twice in the past 6 months, and each time, have renamed my internet to the same name and used the same password.

The past two times I have moved (so for the past 6 months...) I have been unable to connect my printer to the wifi. Every time I want to print (which is daily as I am in school) I have had to preselect all of the documents I want to print, send them to print, then open up HP Smart, press the wifi and cancel button together on my printer approximately three times until the wifi bars are slowly and progressively enlarging, ask HP Smart to find my printer, "Set Up" said printer as a new device, connect to my wifi, input my password, and wait for the items to print. HP Smart is supposed to then continue setting up the printer to use the wifi independently without my computer, but for some reason, it gets stuck on the first step ("Finding the Printer") and never progresses through the remaining steps. So I must then incapacitate my computer to go through this lengthy process every. single. time. I want. to. print. Because it is the only way I can seem to get the printer to produce any requested projects at all. Please. Take me out of my misery and explain how we can resolve this once and for all in the most simplistic step by step way possible. As if you were explaining something to a kindergartner who has never touched a computer before.