Norma if you want to try burning charcoal in the grill you can buy a 10# bag at Walmart for around $6.50. Look for Royal Oak lump charcoal. Making your own charcoal is more trouble than it's worth.
If you wrap some wood with aluminum foil and put it in the grill you'll get smoked pizza which is generally not liked by many. That light smoky flavor from coal is good but smoking pizza using wood tends to give too heavy a smoke flavor.