Purchase insulation sufficient to meet building codes in your area. The typical R-value, or thermal-resistance value, for an attic is R-30. Standard R-30 batts are about 11 inches thick and are available in pre-cut widths to fit standard joist spacing.
Cut a 2-foot section of unfaced batt insulation, with a sharp utility knife, and insert it between the floor joists in the attic. Push the batt into the narrow space at the sloped edge of the attic. The end of the batt will compress some as you push it into the space, but don’t smash it. The ideal spot for the end of the batt is just above the wall plate.
Lay a longer insulation batt in the same joist space, butting the end of it snugly against the end of the first short batt. The batts should fit neatly between the joists without crushing.
Continue to measure and cut the insulation batts, using short 2-foot batts each time you insert the insulation in the narrow wedge at the side of the attic. Throughout the rest of the attic, you can use longer batts.
Follow the first two steps for inserting short batt insulation into each joist space at the edges of the attic, to block the soffit area. Without the batts as blocks, blown-in insulation can filter down into the soffit space, leaving gaps in the attic insulation.
Blow in cellulose fiber insulation to the depth of 11 inches to achieve an R-30 value. You can rent an insulation blower, with a long hose that reaches from the blowing unit to the attic, from a construction rental store or lumberyard.
Ask an assistant to turn on the blower while you’re in the attic with the hose. The insulating fiber doesn’t blow out as much as it lightly drops out, allowing you to direct the insulation between the joists to the desired height.