Take the flat shovel and begin removing the nails on the broken shingle. You may be able to re-use those nails.
Use the broken shingle and a tape measure to measure out the size of the replacement shingle. Cut the replacement using the utility knife. Discard the broken shingle.
Place the newly cut replacement shingle where the previous one was. Lift the shingle in the row above in order to tuck the new one under it. Fitting it exactly where the broken one was is very important.
Secure the new shingle into place. Hammer the roofing nails through the previous holes in the roof to hold down the new shingle.
Lift up the edge of the new shingle so you can spread some roofing cement underneath. Press down for a minute or two to secure the shingle.