|Briefly, from memory--
Remove the front bumper if desired. Remove the mesh 'grille' at the front of the radiator opening -- it's held on by just a few sheet metal screws. Slightly loosen but do not remove the two oil hoses where they connect to the oil cooler.
Unbolt the oil cooler mounting brackets from the bodywork. Lift the oil cooler, and place a large undamaged sheet of aluminum foil on the upper side of the bodywork in front of the radiator and beneath the cooler. Raise the edges of the foil to form a box, and shape the front center section of the foil into a trough. Place a large (1-gallon) catch pan under this trough.
Next, undo the two oil hoses and let them drain onto the aluminum foil and thence into the catch pan. Move the oil cooler out of the car, upend it, and let it drain into the catch pan. Clean up any spills, and dispose of the oil and oily foil in a suitable manner.
When reinstalling the oil cooler, attach it to the bodywork first, then install the hoses, and finally tighten them. Add oil to the crankcase to bring the level up to the 'full' line. Start the engine and ensure that you get oil pressure (which will take somewhat longer than usual), then let it idle and check constantly for leaks. After a minute, stop the engine, wait a few minutes, then top up the oil level to about halfway between the 'add' and 'full' marks. Restart the engine and let it reach operating temperature while checking for leaks.