If you have dark stains (which are usually from dog urine), then those will not come out and that section should be replaced. 

Then use UV light to check for urine stains.

We purchased a property that previous owners had recarpeted and painted but has an awful urine smell.

Hoping to get them all installed next week.Plus odor removal (smoking in 2 units with acoustical ceilings removed and that will be replaced, plus kilz everywhere on the floors and walls, and what smells like a dead dog, with urine and feces in another apartment), completed carpet removal and am starting painting and need new appliances.Oh, and some electrical things are on movable plywood panels, that will need to be dealt with.Pretty total rehab. 

One deal I had a few years back made your eyes start to water 5' from the front door because of the urine smell. 

I got free lunches at school and My mom drove us around our small town in a cat urine yellow 78’ 4 door ford Ltd which was really out of date by the 90’s .

I immediately started cleaning up the place, there were cobwebs everywhere and the place smelled really bad due to urine soiled carpet throughout.

You need to learn how to determine market value, how to advertise, how to pre-screen and screen, how to protect against predator tenants, how to deal with late rent or unauthorized tenants or pets, what you need to know about lead paint or mold or ice dams or furnaces or pet urine on the lawn...If everything goes right, you rent the place one day after advertising, a little old lady moves in, and she pays rent without fail for 30 years at market rates and you walk away a winner.The more likely scenario is that you'll enroll in the school of hard knocks and be beaten back and forth many times before getting it right, losing thousands or tens of thousands in the process. 

Animal urine, torn up carpet, scratches on doors and trim, chewed up trim, dug up lawn.What would it cost to repair?

I would add where they are to walk the pet, immediate clean up of all feces, watering down any urine on the grass before it makes a yellow spot, etc.