It is indeed a complex task. If you search around on the Teline IV forums you will find many threads where people have attempted this.
If I were doing it I would make a backup of my live site using Akeeba backup then install that backup on my localhost using something like Wamp or Xampp.
The menu structure is quite different on T4 as well as a lot of setup options so I would be inclined to also install a quickstart of Teline IV on my localhost then migrate the data accross rather than trying to upgrade a site to T4. There are tools available on the JED for data migration and with a little effort I can see no reason why that method would not work.
Once I have my new site working on localhost I would then use akeeba once again to move my new site to my live hosting.