To recharge an enchanted weapon, you must open your inventory and select the weapon. At the bottom of the inventory screen, your game will list the button used to trigger a recharge- on the computer, this defaults to the ‘T’ key. When you recharge the enchantment on a weapon, you consume a soul gem and the soul within, restoring the enchantment to a degree determined by two factors: the ‘size’ of soul used to enchant the item in the first place, and the ‘size’ of the soul being used to recharge it. Generally speaking, this is where petty souls are best used aside from ‘grinding’ experience in Enchanting- while their recharge amount is small, they are the easiest souls to come by. Additionally, using a soul to recharge a weapon that is of a higher quality than the soul used to enchant the weapon can be very wasteful, as you do not gain any benefit from attempting to exceed the number of charges placed in the weapon on its creation.
As using a soul gem with a soul in it for any purpose consumes it, and each gem only holds one soul regardless of whether or not that soul matches the gem’s capacity, Azura’s Star and Black Star are highly coveted soul gems, being the only two that are not consumed by use. Unfortunately for any Dovahkiin, only one of these can be obtained in the game, and you will have to choose which you prefer. Technically speaking, the Black Star is superior, as Black Souls are the most powerful type of soul, but those attempting to play a more moral Dovahkiin will likely find themselves with Azura’s Star in its stead.
This is because of the way souls are categorized. Petty souls are the souls of common and not terribly powerful creatures- skeever, foxes, wolves, dogs, if it’s more of a speedbump than an obstacle, chances are it has a petty soul. Lesser souls belong to more dangerous things, but still not ones of terribly impressive nature. Larger frostvenom spiders, weaker bears, frost wolves, and chaurus often have this soul type. Common souls are often found in high-end predators such as saber cats or cave bears, as well as some of the more powerful draugr (despite common draugr and animated skeletons lacking souls altogether), and the greater and grand souls are found in only the most dangerous non-player-race foes: giants, some of the unique undead, hagravens, and Dragon Priests. Black souls are found only in the intelligent races- man, mer, khajiit, and argonian all have black souls, and it is considered a sin of the highest order to use these souls for enchantment, as it consumes them and prevents the dead passing on to the afterlife.