How do I recharge. My Honed Greatsword of Burning?

Just go to your weapon inventory, have filled soul gems ready to use (petty, lesser, common, greater, grand, black, azura's star) and recharge the item. The higher the soul gem, the more it will recharge. If you don't want to constantly lose soul gems, get Azura's star. It's a daedric artifact that has unlimited use, it will not disappear after you use it to enchant or recharge items.

You dont need to go to an Enchanting table to recharge. Simply Pick up some soul gems and go to the weapon you wish to recharge. There should be an option that says to recharge if ( If xbox should be RB) not sure for PC or Ps3. Hope This Helps! :)

You do this with soul gems. First, you need a soul gem. A soul gem that is filled with have the type of soul its filled with behind it in parentheses. This would look like Lesser Gem(Lesser). After you have one of these gems (they can be bought at general stores or from mages) you can use them by going to your weapon, then click the charge button (listed at the bottom of the screen), and a list of your available gems will come up. Simply choose which gem you wish to use and your sword will charge! To fill your own soul gem, find and empty gem, then kill an enemy with a weapon that has an enchantment that takes souls, and that will fill the gem. Hope this helps!