You failed to provide any information about the vehicle you are working on.
The new compressor should come with documentation saying whether it is pre-loaded with oil, or how much oil and what viscosity needs to be added. You should also replace the drier and add about an ounce of oil to make up for what's there.
If your old compressor failed internally you also need to replace the condenser and expansion valve or orifice tube, and flush out the rest of the system. After doing that you need to add the total amount of oil specified for your AC system, which should be on a sticker under the hood. (This total amount includes what is in the compressor.) You will probably find doing this is required for the new compressor's warranty.
@chucktobias Thank you Chuck! So, for my 2006 Jeep Liberty, is evacuating the system with a pump, as Scotty teaches us, the same as flushing out the system? If not, what is flushing? And again, does evacuating the system remove all the oil?
Thanks for your patience
So, for my 2006 Jeep Liberty, is evacuating the system with a pump, as Scotty teaches us, the same as flushing out the system?
No.
If not, what is flushing?
Flushing all the old oil and any debris out of the system with a flushing tool and solvent made for AC systems. Most are powered by an air compressor but there are some out there in aerosol cans. I've also heard of mineral spirits being used with a flush kit, but I've never tried that, have always used purpose-made AC flushing compound.
https://www.amazon.com/Conditioning-Pipeline-Cleaning-220PSI-Fittings/dp/B0BKP9F531
https://www.amazon.com/TSI-Supercool-FFQ-High-Temp-Greater/dp/B00CFQQX5S
When using an air compressor to power a flush tool, a drier should be used in the line to remove moisture and oil much as you would do when painting. Also note that the parallel-flow condensers used with R134a cannot be successfully flushed, they must be replaced if the compressor fails and spreads debris into the AC system. The expansion valve should keep debris out of the evaporator, but if easy to get to and not too expensive it would not be a bad idea to replace that as well.
I'll be doing this to my own AC soon, an o-ring blew out emptying the system. Since it is now exposed to atmosphere I'll be replacing the drier, flushing out all the old oil, and putting in the correct amount of fresh oil and refrigerant. (Note that you don't flush the compressor. Dump the old oil out of it to measure and put the same amount back in, distributing the rest required in other parts of the system.) Since the AC system self-evacuated I'll also be taking the opportunity to replace old hoses. If any of yours are questionable, being 18-19 years old, now would be the time to do it. (Fortunately in this heat wave I have other vehicles with working AC that I can use.)
does evacuating the system remove all the oil?
No.
Bear in mind the drier should not be exposed to atmosphere any longer than necessary to bolt it up so it is not saturated with moisture. (It comes sealed with an inert gas inside.) Likewise the PAG oil absorbs moisture that can form acids in the system, so it should be added just prior to pulling vacuum to minimize the problem.
Although not rocket science there is a fair amount to working on air conditioning that is different than other wrenching. If you're really not familiar with it and don't have anyone to guide you hands-on you might want to consider letting a shop do the work. It is all too easy to screw things up or even injure yourself. (Always were eye protection when working on AC!)