When I am recharging weapons, how am I supposed to know the soul gems that have souls I've trapped in them? Also, where can I find the spell "Soul Trap"?
If a soul gem has a soul in it, the soul will be listed after the gem's name in parentheses, so for example, a petty soul gem with a petty soul in it is a "petty soul gem (petty)".
If you find you've captured a weak soul in a strong soul gem, such as a "grand soul gem (petty)", you can empty the soul gem by dropping it on the ground and picking it up again.
The Soul Trap spell can be purchased from most mages, I believe the mage in Dragonsreach (Whiterun's castle) is the first place you can find it, if you start out following the main quest.
Most of the time, it's easier to use a weapon that has soul trap built in when you want to capture souls, if you're primarily playing as a fighter or archer rather than mage.
When recharging (R2 or RT) it will only allow you to use the gems with souls in them. The power of the soul inside will directly effect how many enchanted uses it will give you. Gems with souls in them also have the level of soul in brackets next to them (if I recall correctly). For example "Greater Soul Gem (Lesser Soul)" is a greater soul gem that is being wasted on a lesser soul.
You can find what level of soul each of the creatures in Skyrim has here.
A few mages that will sell you the spell usually at a good price. I'm pretty sure the mage in Whiterun's castle has one. An alternative is to disenchant and enchanted Soul Trap weapon (that's how I got it).
HINT: A good method for taking souls is to enchant and bow and take animals from a distance. Petty souls are still souls and since their easy to take, you will have piles of them.
Good luck and happy soul taking!