How does one invent a spell?

[allies426]

No: HPFGUIDX 135330

So here is what I have been wondering for a while:  how does 
one "invent" magic, more specifically spells, charms, curses, etc?  I 
can understand how a potion might be invented, mixing various magical 
ingredients together, but not spells. 

Take for example, Snape's sectumsempra.  Did he first decide that he 
wanted a spell that would have that particular effect, and then set out 
to discover the incantation and wand motions that would create it?  Are 
spells something that already exist and just need the correct words to 
unleash them?  And what, exactly, is the difference between a charm and 
a spell?

I really need that Harry Potter Encyclopedia.  :)

Allie