Match the correct igniter with your Kenmore dryer model number. Kenmore is a Sears-specific brand, so your local Sears store or repair shop can help you find the right one, if you are having trouble.
Turn off the gas supply valve to the dryer. Unplug the dryer from it's electrical outlet. Pull the dryer away from the wall so you can work behind it.
Clean any lint or dust that has accumulated behind the dryer with a vacuum or broom. This is a fire hazard, so you should remove it before working on the igniter.
Unscrew the rear panel from the dryer.
Look for the igniter at the base of the dryer near the gas valve and unhook the two wires that connect the igniter to the power terminals. The igniter has a ceramic base, usually white, with two metal prongs sticking out of the end.
Remove the screw that holds the igniter in its bracket, and remove the igniter.
Plug in the new igniter and put it in the bracket. Tighten the screw and replace the dryer's rear panel.