Shut off the power to the circuit that will power the recessed downlight.
Check in the attic to make sure that the area where you intend to place the light does not have any electrical wires in the way.
Use a hole saw and drill to cut a hole in the ceiling at the light location.
From the attic, set the light fixture into position over the hole. The unit should be situated so that it can be secured to a ceiling joist. This will keep the light in position.
Strip 1/2 inch of insulation off of the black, white and green wires of the recessed light.
Connect the green ground wire to the ground wire in the junction box that will power the recessed light.
Connect the white wire of the recessed light to the white wires in the junction box.
Connect the remaining two black wires together. Use plastic twist caps to secure each splice.
Turn the power back on and test the light. If the light works fine, then install the recessed light cover, which comes with most units.