$form changes going from 4.7 to 5.1

A small module I have uses the old $form stuff, but this is causing it to not work after upgrading to 5.1. I tried going through the documentation to see if I could figure out how to update the 4.7 $form code to 5.1 compliant...but I couldn't figure it out mainly due to having no experience with writing drupal modules. Help would be appreciated.

Most of this module is just php/mysql/html that I wrote and can be overlooked:
Module can be found here:
http://neohangout.com/files/drupal/sold.rar or http://pastebin.ca/505942

Thanks!