These are the rules in North Carolina. See your particular state's rules for more details.
For most deliveries, the title will come in a separate mailing about 5 business days later.
Once you have the title, contact your insurance company and get it covered. I usually choose liability coverage only. These are closer to junk than not cars, and the replacement-level insurance can be added on later.
Go to the DMV. Here in central NC you actually have a good option. The privately run license agency in Cary, NC has a group of people who are easy to work with. I've been there more times than I can remember. The line sometimes stretches out the door, but it moves. The place is staffed appropriately, there is nowhere to sit. They are professional though, even with the public and all we bring to them. I've been treated with nothing but consideration.
Bring Cash - at least $200. This way you can have a backup plan if credit cards don't work. For some reason, there is one portion of the process that requires about $17 in cash, every time.
Based on the reactions from the DMV professionals, salvage title transfers are shady. Start the conversion with something like 'Bought this salvage title car from auction to fix it up for fun.', that makes things go smoother. Apparently they have had some behind the scenes training about the malfeasance of salvage title transfers and rebranding. Make it clear that you are keeping the salvage title, and not trying to increase it's value, just having fun fixing it. Do not use the words 'rebuilding' as that has a specific meaning in this context.
You may get a temporary registration tag so you can drive it to the inspection station. Once it is inspected, you'll come back to the DMV to get the permanent tag.
In some cases, the vehicle you bought had it's yearly inspection already done, in which case you'll get the real tag in one visit.
At this point you may be thinking - that sounds miserable, I'd rather not go to the DMV ever. The alternative is what the dealership gives you. Many of those papers you sign are limited power of attorneys so they file all this in bulk for you. That's the value-add you're paying for at the dealership or used car lot. Most of my 'family' cars are purchased from Carmax, which generally speaking has the least-bad of all the experiences. You're still paying thousands of dollars for that convenience in various forms of markups, doc fees, etc. What you get is a drive-off experience after 4 hours and no trips to the DMV.