My 02 Buick LeSabre has oil coming from the radiator into the coolant reservoir. Just recently I had a new motor put in to fix the issue. What would be the best/proper way to flush the radiator? It has a new water pump and thermostat.
Use a coolant flush kit
You can add a 'T' to one of your radiator hoses that allow you attach a garden hose to your cooling system.
Once you have added the 'T' to your system you can run your car and the garden hose simultaneously in order to fully circulate the fluid in your cooling system as well as flush out all of the contents of the system to ensure that any oil in it is completely removed from the system.
Flush it out with a hose (ordinary garden hose will do fine), backwards - so that the water flows though in the opposite direction to which it would do in normal operation. Generally they flow from top to bottom, so you want to flush it from bottom to top - it's often easiest to take the rad out and turn it upside-down for this. Keep going until the water comes out clear.