How does one replace the heating element in an electric kenmore elite dryer model 11085862400?

You will need to tear the whole dryer down, clean it, and re-string the element wire through the ceramic insulators. Be very careful that the wire does not touch the metal anywhere. Make sure all parts are very clean, (wash out ducts) including the blower wheel. Also, buy a new belt ($5.00) and white lithium grease to put in all bearings (available at auto parts stores). If the dryer is not clean and the vent pipe, too, it will fail quickly. Go to YouTube to see how to do it. DrTom4444